Honours modules in Physics and Astronomy Detailed descriptions of honours modules (except projects) are given below. Click on the title in the following list to see details for the module of interest. AS3011 Galaxies .......................................................................................................................2 AS3012 Exoplanetary Science...................................................................................................4 AS3013 Computational Astrophysics........................................................................................5 AS3015 Nebulae ........................................................................................................................7 AS4021 Gravitational Dynamics ...............................................................................................9 AS4022 Cosmology.................................................................................................................10 AS4023 Stars ...........................................................................................................................12 AS4024 Binary Stars and Accretion Discs ..............................................................................14 AS4025 Observational Astrophysics .......................................................................................16 AS4103 Project in Astrophysics 1 ...........................................................................................18 AS5001 Astronomical Data Analysis ......................................................................................19 AS5002 Star Formation and Plasma Astrophysics ..................................................................20 AS5003 Contemporary Astrophysics ......................................................................................22 AS5101 Project in Astrophysics 2 ...........................................................................................23 PH3002 Solid State Physics.....................................................................................................24 PH3007 Electromagnetism .....................................................................................................26 PH3011 Information and Measurement...................................................................................28 PH3012 Thermal and Statistical Physics .................................................................................28 PH3014 Transferable Skills for Physicists .............................................................................31 PH3061 Quantum Mechanics I................................................................................................33 PH3062 Quantum Mechanics 2 ...............................................................................................36 PH3066 Mathematics for Physicists ........................................................................................38 PH3073 Lagrangian and Hamiltonian Dynamics ...................................................................40 PH3074 Electronics .................................................................................................................42 PH3075 Applied Vector Calculus............................................................................................42 PH3101 Physics laboratory 1..................................................................................................43 PH3110 Physics Laboratory ...................................................................................................47 PH4021 Physics of Atoms .......................................................................................................51 PH4022 Nuclear and Particle Physics.....................................................................................52 PH4025 Physics of Electronic Devices....................................................................................55 PH4026 Radio and Coherent Techniques ...............................................................................56 PH4027 Optoelectronics and Nonlinear Optics 1....................................................................56 PH4028 Quantum Mechanics 3 ..............................................................................................58 PH4030 Computational Physics .............................................................................................60 PH4031 Fluids .........................................................................................................................62 PH4032 Special Relativity and Fields .....................................................................................64 PH4034 Laser Physics 1 .........................................................................................................66 PH4035 Principles of Optics....................................................................................................68 PH4036 Physics of Music........................................................................................................69 PH4105 Physics laboratory 2..................................................................................................71 PH4111 Project in Physics 1....................................................................................................74 PH5002 Foundations of Quantum Mechanics ........................................................................75 PH5003 Group Theory.............................................................................................................76 PH5004 Quantum Field Theory...............................................................................................78

PH5005 Laser Physics 2 ..........................................................................................................81 PH5008 Optoelectronics and Nonlinear Optics 2....................................................................84 PH5011 General Relativity .....................................................................................................86 PH5012 Quantum Optics .........................................................................................................89 PH5013 Superconductivity ......................................................................................................89 PH5014 The Interacting Electron Problem in Solids...............................................................91 PH5015 Experimental Quantum Physics at the Limit .............................................................93 PH5016 Biophotonics ..............................................................................................................95 PH5101 Project in Physics 2....................................................................................................96 PH5102 Project in Theoretical Physics....................................................................................97

AS3011 Galaxies Semester: 2 Available: each year Credits: 10 Lecturer: Dr Simon Driver Overview This course studies galaxies beyond our own, including their physical properties, various components (stars, gas, black holes etc.), origins and evolution. The idea of galaxies as the basic 'building block' of the Universe is introduced, and we investigate how galaxy surveys can help measure fundamental properties of the cosmos. New ideas and observations happening at the moment are included throughout the course. Aims and Objectives To use observations and simple interpretation and mathematics to deduce properties of galaxies at a distance. The main objectives are: - to understand the physical scales involved (distances, sizes); - to distinguish between different types of galaxy and appreciate some reasons for their variety and different origins; - to interpret galaxy spectra in terms of the internal dynamics and interactions between galaxies; - to learn about components of galaxies not seen in visible light; - to understand how galaxy surveys are used to measure overall properties of the Universe. Learning Outcomes At the end of the lecture course, students will expect to be able to:

- understand why different galaxy components emit at different wavelengths and relate this to temperature, opacity and redshift; - calculate evolving properties within a galaxy, such as enrichment in heavy elements; - follow simple Fourier transformations and correlation techniques to interpret galaxy spectra and clustering properties; - perform simple dynamical calculations using Newton's law of gravity, Poisson's equation for potential and the Virial Theorem for stability. Synopsis Introduction to galaxy properties (distance, mass, size). Classification of types of galaxy, both morphological and quantitative. Stellar and non-stellar components. Derivation of dynamical tools. Stellar distributions in elliptical and spirals. Dynamics in elliptical and spirals. Galaxy clusters including the Local Group. Clustering as a result of large-scale structure, and dark matter. Overall properties of the Universe from galaxy surveys. Primordial galaxies and active galactic nuclei. Enigmas and new discoveries. Pre-requisites: AS2001 Recommended books Galaxies in the Universe, by Sparke and Gallagher is highly recommended - the course uses much of their notation and the book is a good read. For introductory material, Galactic Astronomy by Binney and Merrifield may be useful. These books are about £24 pounds and £33 in paperback; also readily available second-hand. Tutorials There will be three tutorials, each with a problem sheet; solutions will be discussed as a group rather than handed in.

Assessment: 2-hour examination = 100%; no continuous assessment

AS3012 Exoplanetary Science Semester: 2 Available: each year Credits: 10 Number of lectures:18 Lecturer: Prof I A Bonnell Overview The discovery of extrasolar planets is one of the most exciting advances in modern science. We now know of more than one hundred planetary systems besides our own solar system. Exoplanets can be detected by a variety of techniques, each with their own specific window of opportunity. Together with our solar system, these discoveries offer the chance to construct a comprehensive theory for the origin of planets. Aims and objectives To present an overview of our knowledge of extrasolar planets and their implication for the theories of planet formation. Specifically, to introduce i) the variety of techniques used in planet searches, ii) an overview of the deduced properties of extrasolar planets, iii) star formation and the initial conditions of planet formation, iv) the core-accretion model for planet formation and the physics of dust-grain growth in discs, v) the fragmentation of self-gravitating discs, vi) orbital evolution and migration in planetary systems. Learning outcomes By the end of the module, the student should be able to i) understand the advantages and disadvantages of the various detection techniques used in planet searches

ii) comprehend the implications of the deduced properties on models of planet formation iii) comprehend the global evolution of star formation and its relation to planet formation iv) calculate growth rates of dust-grain coagulation and settling v) estimate the importance of self-gravity in planet formation. Synopsis Exoplanet detection: radial velocity, transits, microlensing, direct imaging, reflected light Properties of exoplanets: masses, orbits (periods, eccentricities); implications for planet formation Star formation; angular momentum conservation and disc formation; angular momentum transport and accretion Core accretion, dust settling and coagulation, planetessimal formation, the role of self-gravity Hill spheres and planetessimal accretion, gas accretion, gravitational instabilities and fragmentation Migration and orbital evolution Assessment 2-hour examination = 100%

AS3013 Computational Astrophysics Semester: 2 Available: every year Credits: 10 Lecturers: Prof I A Bonnell Overview Modern sciences rely on the use of computers to calculate quickly and accurately large numbers of relatively simple operations. In astronomy, this includes extracting meaningful results from observational data and theoretical modelling of complex physical systems. The continual advancement of science necessitates the development of individual programmes to undertake the required tasks.

Aims and objectives To familiarise the student with the techniques and approaches to efficient scientific programming, including the basics of Fortran 90 programming language the importance of structured programming the use of subroutines, loops and logical decision making structures the development of codes to solve specific problems a practical experience in using numerical codes to explore physical systems Learning outcomes The student will learn and have practical experience of programming and the use of numerical codes. Specifically, the student will i) be able to programme in Fortran 90 ii) understand and apply the fundamentals of structured programming iii) the ability to develop, test and debug simple and complex codes iv) use numerical codes to explore physical systems. Synopsis An introduction to programming, Fortran 90, simple codes, input/output Logical decision making, loops, data types structure programming, subroutines and functions. code development and practical examples, mass functions use of numerical codes to explore orbits, the importance of accuracy and errors numerical simulations of exoplanetary systems Assessment The module is assessed continuously.

AS3015 Nebulae Semester: 1 Available each year Credits: 15 Number of lectures: 27 Lecturer: Prof A C Cameron Overview The gas that lies between the stars takes many forms. From the dense, cold molecular clouds in which stars are conceived to the rarefied ionized plasma of HII regions, escaping photons carry information about their nature to distant parts of the Universe, a few of which contain astronomers. Astronomers unravel the nature of these gas clouds by catching photons whose last physical interaction was usually with an atom or ion in the cloud itself. The material with which the radiation last interacted imprints clues to its physical nature on this radiation. To find out the temperature, density, chemical abundance and ionization state of the cloud we must understand how matter behaves in a radiation field: how photons and inter-particle collisions can trigger transitions between different excitation and ionization states in atoms and molecules, and how these transitions create or destroy the photons that we eventually see. Aims and Objectives To present an introductory account of radiative transfer and its application to gaseous astrophysical systems, including • The definitions of the basic radiant quantities and the equation of radiative transfer. • The use of the Boltzmann and Saha equations to compute level populations and ionization equilibria • The Einstein relations and their role in computing line opacities and emissivities, • The Planck function and its properties, • The various types of atomic and molecular line transitions and broadening mechanisms encountered in nebulae, • The application of these theories to molecular clouds, HII regions and planetary nebulae. Learning outcomes By the end of the module, students will have a comprehensive knowledge of the topics covered in the lectures and will be able to: • Define and use the basic radiant quantities such as specific intensity, mean intensity, flux and radiation pressure of a radiation field; • Differentiate and integrate the Planck function to obtain Wien’s Law and the Stefan- Boltzmann Law,

• Use the Boltzmann equation, the Saha equation and the Einstein relations to determine level populations and ionization balance both in and out of thermodynamic equilibrium, • Use the equation of radiative transfer to solve for simple geometries how the emergent intensity of a beam of radiation is modified by emitting and absorbing material along its path, • Define the photon mean free path and optical depth, and distinguish between optically thick and optically thin media, • Distinguish between radiatively and collisionally induced transitions, and state their importance in relation to the global energy balance of a body of gas, • Distinguish between natural, collisional and thermal broadening mechanisms in spectral lines, • State the importance of ionization fronts, use the jump conditions to distinguish between R- and D-type fronts, and understand their importance in the evolution of an HII region. • Distinguish between recombination-spectrum formation in Case A and Case B, and use Balmer-line fluxes and line ratios to determine total ionizing flux and interstellar extinction in Case B, • Use simple atomic theory to demonstrate the usefulness of transitions between low- lying levels of common collisionally-excited species as density and temperature diagnostics in emission-line nebulae, • Use radio brightness temperatures of a background source and foreground nebula to determine nebular temperature, • Distinguish the various types of transition for simple molecules, and state their importance as coolants in star-forming regions. Synopsis Definitions of basic radiant quantities. Opacity and emissivity. The equation of radiative transfer. Source function and optical depth. Black-body radiation and the diffusion approximation. Atomic and molecular processes: bound-bound, bound-free and free-free transitions, electron scattering, Boltzmann and Saha laws, the Einstein coefficients and their relation to emission and absorption coefficients and to blackbody radiation. Masers. Line-broadening mechanisms. Stromgren spheres, protoplanetary discs. Derivation of jump conditions across ionization fronts using conservation of mass, momentum and energy. Thermal equilibrium between ionization and cooling via photon escape in nebulae. Collisional cooling and detailed balance; hydrogen recombination spectrum in Case A and Case B; common line-ratio and radio diagnostics for nebular temperature and density. Rotational and vibrational spectra and selection rules in molecules. Prerequisites AS2001

Recommended books Introduction to Stellar Astrophysics: Volume 2 (Stellar Atmospheres) by E. Böhm-Vitense, is cheap, covers the basics of radiative transfer very well, and is also useful for next year's course on stellar structure. Radiative Processes in Astrophysics, by Rybicki and Lightman, is a standard reference, but goes a long way beyond the scope of this course. It is also expensive and hard to obtain, but is available in the Physics & Astronomy Library. Astrophysics of Gaseous Nebulae and Active Galactic Nuclei, by D. Osterbrock, is also recommended for background Library reading on the various nebular diagnostics discussed later in the course. Tutorials There will be three problem sheets, and at least three whole-class tutorials will be held to discuss these and other more general issues. A sample examination question will be given out and answers will be expected to be handed in by a due date for marking and return. Assessment 2-hour examination = 100% There is no continuous assessment in this module.

AS4021 Gravitational Dynamics Semester: 2 Available: 2007-08 Credits: 10 Number of lectures: 18 Lecturer: Dr. H. Zhao Overview Gravitational Dynamics is the name given to a way of modelling the motions of stars and galaxies in their collective gravitational field. Stars attract each other, and there is also the gravitational effect of the mysterious dark matter. The attraction bends the otherwise straight-line motion of stars into curved orbits. By measuring the motions one can infer the underlying gravitational field and the existence of black holes and dark matter. Gravitational dynamics also tells us how to model the collisions of galaxies, and how gravitational tides tear an object apart. It is an essential framework for quantitative study of motions and force field. Aims and Objectives and Learning Outcomes

1. Analytical understanding of the mathematical relations among various quantities describing • the stellar system: • the star density a function of position in a star cluster, • the gravitational potential and the escape velocity, • the velocity phase space distribution function, • the velocity dispersion and the circular rotation curve, • the pericenter and apocenter of a stellar orbit • conserved quantities (energy and angular momentum). 2. To be able to appreciate the dynamical arguments for the existence of dark matter. Synopsis 1. Potential, gravity force and matter density 2. Distribution functions 3. Equations of motion 4. Jeans equations. 5. Tides and relaxation Prerequisites Ability to differentiate and integrate correctly is essential. Very often in the course you are required to calculate from a spherical density function n(r) to the mass enclosed inside a radius r. Partial differentiation is also used all the time, e.g., the Poisson's equation involves a double partial differentiation of the coordinates x, y, and z. Some basic knowledge of a stellar gravitating system (globular clusters or galaxy) is also assumed. Recommended books Galaxy Dynamics by J. Binney and S. Tremaine, 1987. Tutorials About 4 tutorials spread evenly throughout the course. Assessment 2 hour examination = 100%

AS4022 Cosmology

Semester 2: Available: each year Credits: 10 Number of Lectures: 18 Lecturers: to be announced Overview Einstein describes gravity in terms of mass and energy impressing curvature on the space-time manifold of the Universe. Observations of our Universe show that it is expanding and remarkably homogeneous and isotropic on large scales. The Friedmann equation that governs the evolution of such a universe is remarkably simple. The geometry, current age, ultimate fate, and a variety of observable phenomena, all depend on the current energy densities of radiation, matter, and the vacuum. Constraints on these cosmological parameters arise from observations of the apparent brightnesses and angular sizes of high-redshift objects. The best results currently arise from sound waves in the early universe that leave distinctive patterns in small-amplitude fluctuations on the otherwise isotropic microwave background radiation left over from the Big Bang. These are the seeds that subsequently grew by gravitational instability to form the stars and galaxies that we see around us today. Aims and Objectives To introduce the principal concepts of modern cosmology including: - metrics for curved expanding universes - Friedmann's equation for cosmic evolution - effects of radiation, matter, and vacuum energy densities - observations that constrain the cosmological parameters - acoustic signatures in the cosmic background radiation - cosmic inflation to solve the horizon and flatness problems - the growth of perturbations to form galaxies and large-scale structure Learning Outcomes Students will develop a comprehensive understanding of the main concepts relevant to modern cosmology, and the ability to perform a variety of quantitative calculations relevant to cosmic evolution and measurements of cosmological parameters. Synopsis: - geometry of expanding space-times with constant curvature. - fluxes and angular sizes of high-redshift targets - cosmic eras dominated by radiation, matter, and vacuum energy. - evolution of homogeneous isotropic expanding universes - geometry, age, and fate of different possible universes - observations that constrain the cosmological parameters

- evidence for dark matter and dark energy - gravitational lensing, Sunyaev-Zeldovich effect - creation of light elements in the Big Bang - acoustic oscillations and the cosmic background radiation - cosmic inflation and the horizon and flatness problems - growth of small density perturbations to form clusters and galaxies Tutorials: There will be tutorial problem sets to test understanding of concepts and to develop skill in performing cosmological analysis and calculations. Assessment 2-hour examination = 100%

AS4023 Stars Semester: 2 Available each year Credits: 15; Number of lectures: 27 Lecturer and webpage: K. Wood, http://www-star.st.and.ac.uk/~kw25/ Prerequisites: AS2001 Overview One of the triumphs of 20th century astrophysics is the ability to understand and predict the observable properties of a star and understand stellar evolution. The radiation we observe from stars primarily comes from the outermost layers known as the stellar atmosphere, which is the transition region from the dense interior to the low density interstellar medium. Analysis of the line and continuum spectrum enables us to determine the physical conditions such as the chemical composition and the run of temperature and density in the atmosphere. The stellar interior provides the high densities and temperatures that ultimately lead to the source of stellar energy: nuclear fusion. It is in the interior of stars that most of the elements are created and the stellar mass and energy available determine a star’s evolution and ultimate fate. Therefore to understand stellar evolution we must understand the conditions in stellar interiors by appealing to the physics of radiation transfer in dense environments, thermodynamics, and nuclear physics. Aims and Objectives To use the equations of radiation transfer and hydrostatic equilibrium to determine the structure of a stellar atmosphere and explain the observed line and continuum spectra. To study the structure and source of energy generation in stellar interiors and stellar evolution.

Learning Outcomes By the end of the module the students will be able to: • Solve equation of radiation transfer for static, plane parallel model atmospheres in the

gray atmosphere approximation • Use radiation transfer to explain limb darkening in stellar atmospheres, and

continuum and spectral line formation • Understand the concept of Local Thermodynamic Equilibrium and conditions where it

applies • Understand basic principles behind Monte Carlo radiation transfer scattering codes

including sampling for direction of emission, optical depths, and scattering angles • Outline a Monte Carlo scattering code and develop Monte Carlo estimators for the

intensity moments of the radiation field showing how they relate to formal definitions • Define and be able to calculate Jeans’ masses and densities • Write down and explain the terms in the equations of stellar structure • Understand the equation of state that provides pressure support in stellar interiors • Understand what is meant by a homologous model and apply it to solve the equations

of stellar structure • Understand and describe nuclear cycles in stars including CNO cycle, proton-proton

chain, etc • Understand and describe stellar properties on the main sequence and explain post

main sequence evolution and the fate of stars Synopsis Recap basic definitions of intensity moments, sources of opacity and emissivity, Local Thermodynamic Equilibrium, and the equation of radiation transfer. Approximate solutions of the equation of radiation transfer including optically thin solutions, optically thick diffusion, gray atmospheres. Apply equation of radiation transfer to explain limb darkening, and the observed stellar continuum and line spectra. Constructing a theoretical model atmosphere, incorporating solutions of the equation of radiation transfer, assumptions of LTE, equation of hydrostatic equilibrium. Monte Carlo radiation transfer, sampling from probability distributions, estimators for intensity moments of the radiation field, scattering codes. Fundamental timescales in stellar evolution. Equations of stellar structure, their approximate and numerical solutions. Sources of pressure support in stellar interiors. Thermonuclear reactions. Star formation, properties of stars on the main sequence, and post main sequence evolution. Recommended Books Introduction to Stellar Astrophysics: Volume 2 (Stellar Atmospheres) by Erica Bohm-Vitense. This was used in the Nebula course and will be used here for the stellar atmospheres section and also some of the stellar structure section.

Introduction to Monte Carlo Radiation Transfer by Wood, Bjorkman, Whitney, and Wolff. A short booklet on basic Monte Carlo radiation transfer techniques. Covers everything in the Monte Carlo lectures and can be downloaded from the course webpage. Introduction to the Theory of Stellar Structure and Evolution by Dina Prialnick. Very good text for stellar structure, thermonuclear reactions, and stellar evolution. Tutorials There will be at least three problem sheets and three whole-class tutorials. It is expected that the problems will be attempted before the tutorials during which the problems will be worked through along with discussions of any other aspects of the course. Assessment Two hour examination = 100%.

AS4024 Binary Stars and Accretion Discs Semester: 1 Available: 2007-08 Credits: 10 Number of lectures: 18 Lecturer: to be announced Overview Any sensible theory for the formation of stars must be able to explain why binary stars should occur so frequently. The binary nature of these systems can influence very drastically the ways in which the component stars evolve from the zero-age main sequence through to their end states, with the result that many strange stellar phenomena are found to occur only in binaries. Additionally, binary stars are the only source for empirically-determined stellar masses, and the primary source for stellar sizes. This module explores the observational and analysis methods for establishing the properties of binary stars. Aims and Objectives Since binary stars are as common as single stars in the universe, it is appropriate that there should be a whole module devoted to their study. This module discusses: two-body orbital motion, methods for dstermining orbits from velocities, pulse-timing, and spatially-resolved systems, analyses of light curves, and the resultant masses, radii, and luminosities of stars of all types found in binaries - from pre-main-sequence stars to neutron stars and black holes. The module also presents accounts of theoretical models and observations on the processes of mass exchange and mass loss in binaries including accretion discs, streams, and outflows.

Learning Outcomes By the end of the module, students will have a comprehensive knowledge of the topics covered in the lectures and will be able to .. calculate velocities and positions as a function of time in any closed orbit, and light-time advances and delays for pulsed sources in orbit .. calculate potentials for non-spherical bodies, and understand the production of tides, and the long-term effects upon orbits of perturbing potentials, including general-relativistic terms .. understand the shapes of light curves for eclipsing binaries, calculate approximate stellar sizes and orbit orientations from a simple model, and appreciate the numerical methods required to make full calculations of light curves from theoretical models .. understand the Roche model for binary stars, and its importance in calculating stellar evolution models for binary stars; calculate amounts of mass exchanged between components or lost from the binary system from observed changes in orbital periods .. understand the processes of mass exchange with streams, impact regions, accretion discs, and appreciate the numerical methods used to establish images of such sources in binary systems. Synopsis Introduction - types of binary stars A resume of Newtonian gravitation Orbits in the two-body problem Application to spectroscopic binaries Measuring radial velocities and orbital periods Determination of the elements of spectroscopic orbits Pulsars - pulse timing and binary orbits Perturbed two-body motion Potentials for non-spherical bodies, with applications to the Earth's tides and to binary stars The Roche model for binary stars Light curves of binary stars; masses and other astrophysical parameters Roche lobe overflow (RLOF)

Mass exchange and mass loss from binary systems Accretion processes Imaging stellar surfaces and accretion structures Accretion on to the accretor Prerequisites AS2001 for an understanding of stellar structure and evolution, AS1001, PH2011, and MT2001 for basic gravitational dynamics Recommended Books The principal text is An Introduction to Close Binary Stars by R W Hilditch (Cambridge, 2001), which covers considerably more than this basic course; the most relevant parts are: chs.1,2,3(part),4,5(part), 6,7(part). Additionally, some parts of chs.1,4,5,6 of Accretion Power in Astrophysics by Frank, King & Raine (Cambridge, 2003) are helpful. Tutorials There will be three problem sheets, and at least three whole class tutorials will be held to discuss these and other more general issues. Sample examination questions are included with the tutorial sheets. Assessment 2-hour examination = 100% There is no continuous assessment in this module.

AS4025 Observational Astrophysics Semester: 1 Available each year Credits: 15 Number of Labs: 22 plus evening observing sessions Lecturer: Prof A C Cameron/Dr S P Driver Overview Astrophysics is an observational, rather than an experimental, science. Nearly all the information that astronomers can gather about the Universe at large and the objects within it, comes to us in the form of electromagnetic radiation. Today it is possible to study distant objects over nearly the entire electromagnetic spectrum from gamma rays to radio waves.

Optical ground-based observations, however, remain the “workhorse” form of observation, providing the context within which observations at other wavelengths are often interpreted. Spectroscopy allows us to determine properties such as temperatures, elemental abundances and radial velocities. Photometry allows us to explore the structure of spatially-resolved objects such as nebulae or galaxies via direct imaging, or to study the evolutionary properties of stellar populations via colour-magnitude diagrams. With a little extra ingenuity, spectroscopic and photometric monitoring of variable objects gives important physical insight into their detailed physical structure. Aims and Objectives The aim of the Astrophysics Laboratory modules is to familiarise students with a wide range of basic problems and techniques in astronomy and astrophysics, while allowing the pursuit of individual practical interests. Students will gain experience in the application of many skills including astronomical observations, measurement, data analysis via various software packages, and the writing of reports. Learning outcomes By the end of the module, students will have a comprehensive knowledge of basic ground-based observational techniques and data-analysis methods and will be able to:

• Plan a set of observations, selecting a suitable set of astronomical objects that will be accessible from an observatory at a given latitude at the time of year concerned ,

• Calculate the appropriate exposure times for the targets’ brightnesses and select the appropriate lunar phase,

• Operate the telescopes at the University Observatory competently and safely, • Acquire digital images and spectra and transfer them to other computers for off-line

analysis, • Extract point-source fluxes, wavelength-calibrated spectra and surface-brightness

profiles of extended objects from raw data frames using standard astronomical software packages in the Starlink Software Collection under the Unix operating system,

• Perform subsequent analyses such as measuring stellar radial velocities via cross-correlation and constructing an empirical colour-magnitude diagram, again using standard software and graphics packages

• Use these measurements to test theoretical understanding of pulsating stars, stellar evolution and galaxy profiles.

• Record and write up results in a professional manner. Synopsis This is an observational and laboratory-based module that introduces students to the hands-on practical aspects of planning observing programmes, conducting the observations, and reducing and analyzing the data. Observations are secured at the University Observatory using various telescopes for CCD photometry of star clusters and galaxies, and for CCD spectroscopy of stars. Further sources of data may be made available from international

observatories. Students gain experience in observation, data analysis, the UNIX operating system, standard astronomical software packages, and report writing. Prerequisite AS2001 Recommended books Appropriate user manuals for the operation of telescopes and data analysis packages are provided during the evening observing sessions and in the laboratory. Laboratory Hours Tuesdays and Thursdays: 14:00 to 17:30, starting in the Honours Laboratory promptly at 14:00. A member of staff or demonstrator will be present to check on the progress of the various assignments, and to provide help where necessary. Assessment Continuous assessment = 100%

AS4103 Project in Astrophysics 1 Semester: whole year Available each year Credits: 30 Overview The project aims to develop students’ skills in searching the appropriate literature, in experimental and observational design, the evaluation and interpretation of data, and the presentation of a report. The main project is preceded by a review essay. There is no specific syllabus for this module. Students taking the BSc degree select a project from a list of those available and are supervised by a member of the academic staff. Students taking an MPhys degree are not normally permitted to do this module. Assessment Project and oral examination = 100%

AS5001 Astronomical Data Analysis Semester: 1 Available: each year Credits: 15 Lectures: 27 Lecturer: Prof Keith Horne Overview Astronomers and other physical scientists fit models to quantitative observational or experimental data in order to answer questions about the physical world. Data are always affected by measurement errors, leaving uncertainty in the answers to questions posed. Probability theory provides a precise language for discussing and expressing those uncertainties. Statistical data analysis provides practical tools for posing questions and teasing answers from the data. Analysis of real datasets is the best way to build expertise in quantitative data analysis. Aims and Objectives To develop an understanding of basic concepts and offer practical experience with the techniques of quantitative data analysis. Learning Outcomes By the end of the module, students should be comfortable with the concepts of probability theory and statistics, familiar with techniques for quantitative data analysis, and confident in their ability to tackle data analysis problems in astronomy or wherever they may arise in their future work. Synopsis Beginning with fundamental concepts of probability theory and random variables, practical techniques are developed for using quantitative observational data to answer questions and test hypotheses about models of the physical world. The methods are illustrated by applications to the analysis of time series, imaging, spectroscopy, and tomography datasets. Students develop their computer programming skills, acquire a data analysis toolkit, and gain practical experience by analyzing real datasets. The module is assessed continuously on the basis of exercises and projects. Prerequisites AS3013 (Computational Astrophysics) or PH4030 (Computational Physics).

Familiarity with a programming language and concepts of computational physics or astrophysics are assumed. Recommended books Numerical Recipes, the Art of Scientific Computing by Press, Flannery, Teukolsky, Vetterling (Cambridge University Press) Tutorials Tutorials and consultation will be available, especially in the latter part of the course when students are working on their data analysis projects. Assessment Continuous assessment -- 100% based on problem sets and two projects involving computer programming analysis of data sets from the Hubble Space Telescope and the Keck 10m telescope.

AS5002 Star Formation and Plasma Astrophysics Semester: 2 Available: each year Credits: 15 Number of lectures: 27 Lecturer: Dr. M. Jardine Overview The interaction of a magnetic field with an ionised gas (or plasma) is fundamental to many problems in astrophysics. Star formation in particular is heavily influenced by the magnetic fields of molecular clouds, and once stars form they can, if they posses a convective region, generate their own magnetic fields by dynamo activity. The behaviour of this magnetic field is at the heart of many of the most interesting observations of young stars and their accretion disks. Aims and Objectives To present an account of the theory and observations of magnetic activity in solar-like stars, including

• an introduction to magnetohydrodynamics

• the physics of heating stellar coronae to temperatures of 106K

• propagation of information in a plasma by magnetohydrodynamic waves

• the generation of stellar magnetic fields by dynamo action

• the role of magnetic fields in star formation

• the physics of accretion disks

• stellar spin down by accretion disks and stellar winds. Learning outcomes By the end of the module students will have an understanding of the physics of stellar magnetic fields as presented in the lectures and will be able to • Describe the main observational signatures of magnetic activity • Use the magnetohydrodynamic equations describe the behaviour of simple magnetic

field configurations • Give an account of the heating of stellar coronae and derive the scaling relations for

pressure, temperature and length of magnetic loops • Describe the characteristics of the three MHD wave modes and use this knowledge to

analyse information travel for different magnetic field configurations • Describe the main observational features of solar and stellar dynamos and calculate

the characteristics of a simple kinematic solution • Use the Virial theorem to explain the characteristics of magnetic support of molecular

clouds and the onset of cloud collapse. • Demonstrate the role of viscosity in accretion disks and determine the temperature

profile of such a disk. • Use torque balance in an accretion disk to explain stellar spin-down by star-disk

coupling. • Use conservation of mass and momentum to derive Parker's wind solution and

describe the role of magnetic channelling in a rotating star. • Determine the angular momentum loss rate for simple examples. Synopsis Review of observations of stellar magnetic activity

Equations of magnetohydrodynamics (MHD) Heating of stellar coronae. Reconnection. Energetics of coronal loops and the role of rotation MHD waves and propagation of information Solar and stellar dynamos (mean field models) Star formation: properties of magnetic cloud cores, magnetic support and the Virial theorem Accretion disks: transport of mass and angular momentum, role of viscosity. Temperature profiles. Stellar spin down by magnetic star-disk coupling. Rotation distributions of young solar-type stars. Magnetic braking by stellar winds Prerequisities AS2001 Recommended Books Plasma Physics by P.A. Sturrock (CUP) Accretion Power in Astrophysics by J. Frank, A. King and R.J. Raine (Cambridge Astrophysics series 21) The Physics of Fluids and Plasmas by A.R. Choudhuri (CUP) Introduction to Stellar Winds by H. Lamers and J. Cassinelli (CUP) Stellar Magnetism by L. Mestel (Clarendon Press, Oxford) Tutorials There will be four problem sheets, and four tutorials will be held to discuss these and other more general issues. Assessment 2-hour examination=100% There is no continuous assessment in this module.

AS5003 Contemporary Astrophysics Semester: 1 Available: each year

Credits: 15 Number of lectures: 27 Lecturers: Prof I A Bonnell and others Overview Astrophysics is a constantly changing field in which new observations and theories are continually revising our knowledge and outlook. This course provides a view of research level astrophysics and the opportunity to apply the accumulated knowledge of the astrophysics degree to new problems. Aims and objectives To introduce the student to research level astrophysics including several independent topics of current research. To use the knowledge base, applied to novel problems. Learning outcomes: The student will be able to use his/her accumulated knowledge and apply it to topics of current astrophysical research. Specifically, the student will be able to

• comprehend the primary concepts in research level astrophysics topics;

• formulate an approach to novel and unsolved problems;

• understand the different techniques and approaches used in various topics;

• make critical judgement of the merit of research papers in astrophysics. Synopsis: This is a continually evolving module that introduces the student to three main topics of astrophysical research. Topics covered can include dynamics, star formation, X-ray astronomy, gravitational microlensing, stellar winds, interacting binaries, AGN, galaxy formation and evolution. Assessment 2-hour examination = 100%

AS5101 Project in Astrophysics 2

Semester: whole year Available each year Credits: 60 Overview The project aims to develop students’ skills in searching the appropriate literature, in experimental and observational design, the evaluation and interpretation of data, and the presentation of a report. The main project is preceded by a review essay. There is no specific syllabus for this module. Students taking the MPhys degree select a project from a list of those available and are supervised by a member of the academic staff. Assessment Project and oral examination = 100%

PH3002 Solid State Physics Semester: 2 Available: each year Credits: 15 Number of lectures: 27 Lecturer: Dr F Baumberger Overview Solid state physics is primarily the study of the properties of the dense assembly of electrons that is formed by placing atoms in close proximity to one another in a solid. The importance of the subject stems from the fact that these electronic properties underlie just about all of modern technology. For example, they determine the strength of materials and how they interact with light. Most important of all, they govern how the materials conduct electricity, and therefore how to design the electronic circuits that give us computers, the internet etc. The subject is therefore important technologically, but it is also fascinating from the standpoint of pure physics. There would be no possibility of understanding the properties of metals, semiconductors and insulators without the ideas of quantum physics; indeed this is perhaps the earliest chance for the honours physics student to see those ideas applied in a situation where their consequences are so profound. Aims and Objectives To set up the simplest ‘independent electron’ quantum mechanical theory of electrons in solids: The classical Drude model of metals: successes and failures.

The quantum Sommerfeld model of free electrons and the importance of the Pauli exclusion principle.

Brief introduction to the ideas of periodicity and crystallinity. Nearly Free Electron theory: perturbation theory of the effect of the ions of the crystal array.

Tight binding theory: perturbation theory of the formation of a crystalline from an assembly of isolated atoms.

Thermal physics of lattice vibrations. The role of the Fourier transformation in solid state physics. The importance of the Fermi velocity and its relationship to effective mass. Learning outcomes Students taking this course should emerge with a good understanding of some of the fundamental issues of modern physics:

Why a material can contain electrons moving at a significant fraction of the speed of light but still be an insulator. The utility of the Fourier transformation not just in solid state physics but in other fields

Why quantum mechanics is not just an esoteric theory but a practical and vital one. An appreciation of the limitations of the independent electron approximation. An idea of the philosophy adopted in more advanced quantum field theories. Synopsis The classical Drude model of metals and its predictions for the electrical and thermal conductivity and specific heat. The Sommerfeld model – solving the Schrödinger equation for a particle in a box and then filling the allowed states subject to the constraints of the Pauli exclusion principle. Periodic versus fixed wall boundary conditions. The consequences of the Pauli principle and the concepts of the Fermi surface, Fermi velocity, Fermi energy and Fermi temperature. The failure of even the quantum model to predict the Hall effect. Introduction to quantum mechanical perturbation theory and its application to the two limits of a very weak and a very strong lattice potential. The classical and then quantum theories of lattice vibration. The concept of the phonon. How the Fourier transform and the convolution theorem bring elegance to solid state and other fields of physics. Using our knowledge to calculate the properties of real metals and semiconductors. The concept of the electrons and holes, and a discussion of effective masses. The origin of a positive Hall coefficient. The importance of Fermi surface integrals of powers of the Fermi velocity. Prerequisites The first semester JH courses in quantum mechanics and thermal physics (or their equivalent for any students doing only the second semester in St. Andrews). Some quantum physics, e.g. the Pauli principle and perturbation theory, will not have been studied before; a brief general introduction will be given during the course. Recommended books The principal book is Solid State Physics by Hook and Hall (Wiley 1991). Another book at about the same level is Kittel, Solid State Physics (Wiley) although out-of-print earlier

editions are preferable to later ones. For reading around the subject, more advanced books such as Ashcroft and Mermin, Solid State Physics (Saunders), Ibach and Luth, Solid State Physics (Springer Verlag), Singleton, Band Theory and Electronic Properties of Solids (Oxford) and Ziman, Theory of Solids (Cambridge) are also both useful and a good future investment. Tutorials The course includes six tutorial sheets comprising a total of twenty-seven problems. These form an important complementary source of information, and will be discussed during six whole class tutorials. Assessment 2 hour examination = 100%. There is no continuous assessment in this module, but the examination often covers some concepts covered in tutorial problems rather than lectures, and essay-type exam questions may be used.

PH3007 Electromagnetism Semester: 2 Available: each year Credits: 15 Number of lectures: 27 Lecturer: Dr C J Pickard Overview Starting from fundamental experimental observations, the properties of electric and magnetic fields are explored. Solutions to electric and magnetic problems in a variety of dielectric, conducting and magnetic media are investigated. The basis of the subject, Maxwell’s equations, are derived and shown to lead to wave equations which describe electromagnetic radiation. The theory is applied to the transmission of electromagnetic waves in various media. Aims and Objectives To develop an appreciation of the fundamental physics involved in electric and magnetic phenomena, to develop methods for determining the fields and potentials associated with electricity and magnetism and the relevance of these concepts to electromagnetic radiation, including • vector analysis - the mathematical basis of the subject, • electrostatic fields, • dielectrics,

• magnetic fields of steady currents, • Maxwell’s equations and their applications, • plane electromagnetic waves in free space and in matter, • radiation of electromagnetic fields. Learning Outcomes By the end of the module, students will have a comprehensive knowledge of the topics covered in the lectures and will be able to • apply vector analysis and differential calculus to solve problems in electromagnetism, • derive the Maxwell equations and the wave equation, • use special techniques to solve problems in electrostatics, such as the method of

images and Laplace’s equation, • calculate electric and magnetic fields in free space and in matter, • describe and understand propagation of electromagnetic waves in free space and in

matter. Synopsis Vector algebra, differential calculus, integral calculus, curvilinear coordinates. Electrostatics. The electric field, electrostatic potential, Coulomb’s and Gauss’s laws. Dipoles and multipoles. Laplace’s equation. The method of images. Conductors. Dielectrics. Electric fields in dielectrics. Polarization. Magenetostatics. Magnetic fields of steady currents. The Lorenz force. Magnetic torque. Magnetic fields in matter. Diamagnetics, paramagnetics, ferromagnetics. Electrodynamics. Maxwell’s equations. Electromagnetic induction. The wave equation. Electromagnetic waves in free space. The Poynting vector. Propagation of the electromagnetic waves in matter. Reflection and transmission. Absorption and dispersion. Radiation of electromagnetic waves. The electromagnetic potentials V and A (the vector potential). Electric dipole radiation.

Prerequisites There are no prerequisites other than an elementary knowledge of electricity and magnetism - which students will have obtained in the Physics 2B module or elsewhere. Recommended books The principal book is Electromagnetic Fields and Waves by P Lorrain and D Corson (Freeman 1970) or its earlier edition, Introduction to Electromagnetic Fields and Waves by D Corson and P Lorrain (Freeman 1962). Much of the book is directly relevant to the course, and the remaining chapters offer a good introduction to classical electrodynamics. Alternatively, Introduction to Electrodynamics by D J Griffiths (Prentice Hall 1999) can be used, which gives a good introduction for the early sections on vector analysis. The most classical but more challenging book on electromagnetism is Classical Electrodynamics by J D Jackson (Wiley 1999), which will be partially used in the course. Tutorials There will be three problem sheets, and at least three whole class tutorials will be held to discuss these and other more general issues. A sample examination question will be given out and answers will be expected to be handed in by a due date for marking and return. Assessment: Continuous assessment = 25%, 2-hour examination = 75%.

PH3011 Information and Measurement Description not yet available

PH3012 Thermal and Statistical Physics Semester: 1 Available: each year Credits: 15 Number of lectures: 27 Lecturer: Dr S A Grigera Overview Thermodynamics and statistical mechanics provide complementary approaches to understanding many-body states of matter. This course introduces the fundamental ideas and

methods of both approaches and applies these to systems in thermal equilibrium, covering systems of both quantum mechanical and classical particles. Physical examples are used throughout to develop the ideas in a concrete way. Aims and Objectives To present the fundamental ideas and methods of statistical mechanics and thermodynamics, and to develop these through simple examples and applications. The presentation includes: • Laws of thermodynamics • Thermodynamic potentials and Maxwell’s relations • Application to simple thermodynamic systems • Microcanonical ensembles and Boltzmann entropy • Canonical ensemble and Helmholtz free energy • Grand canonical ensembles and chemical potential • Counting for particles with quantum statistics • Important examples of statistical mechanics: paramagnet, heat capacity in crystals, ideal classical and quantum gases, Bose-Einstein condensation, and electrons in metals. White dwarfs and neutron stars. Learning Outcomes On completion of the module, students will attain an understanding of the fundamentals of equilibrium statistical and thermal physics, appreciate its range of applicability, and be able to solve a wide range of elementary problems. They will • Understand and be able to explain the assumptions inherent in equilibrium thermodynamics and statistical physics • Select approaches appropriate to common problems • Be able to apply thermodynamics to simple systems • Calculate the statistical weight and entropy for multilevel systems • Understand the application of partition functions to multilevel systems and dispersive particles and be able to apply these to standard situations • Be able to apply the Gibbs formulation to basic scenarios • Develop an understanding of the characteristics of Fermi-Dirac and Bose Einstein statistics and the their implications for stars, metals, and quantum liquids Synopsis Zeroth and first laws of thermodynamics, ideal gas illustrating a simple equation of state, thermal equilibrium, quasistatic and reversible processes. Microstate, macrostate, statistical weight, postulate of equal a priori probability, equilibrium postulate, Boltzmann form for the entropy. Second law of thermodynamics. Microcanonical ensemble.

The Boltzmann distribution, partition function, general definition of the entropy, Helmholtz free energy. Canonical ensemble. The statistical mechanics of a two level system. Negative temperature. Fundamental thermodynamic relation. Maxwell’s relations. Overview of the thermodynamic potentials. Conditions for equilibrium. 3rd law of thermodynamics. Thermodynamics applied to heat engines and refrigerators. Properties of perfect and real gases. Adiabatic cooling. The heat capacity of a crystal using the method of the canonical ensemble. Einstein model : a multi-level system using statistical mechanics. Debye model : density of states and degeneracy. Ideal classical gas at high temperature. De Broglie wavelength and quantum behaviour. Introduction to phase space. Quantum statistics: Bose-Einstein and Fermi-Dirac. Identifying which statistics apply to fundamental and composite particles. The partition function for an ideal quantum gas. Application of quantum statistics to light. Black body radiation of a gas of photons. Derivation of physical properties. Systems of variable particle number. The Gibbs distribution and chemical potential. The grand partition function and the grand potential. Grand canonical ensemble. The Fermi-Dirac and Bose-Einstein distributions for a perfect quantum gas. Implicit determination of the chemical potential. Application to important systems including metals, Bose-Einstein condensation in quantum fluids, white dwarves and neutron stars. Recommended Books F. Mandl, Statistical Physics, Wiley The course content and level matches this book so it is very highly recommended. The few extra topics such as neutron stars not covered are dealt with in detail in lecture notes. Further reading: These books may aid your understanding: David S. Betts and Roy E. Turner, Introductory Statistical Mechanics, Addison-Wesley (1993). R. Bowley and M. Sanchez, Introductory Statistical Mechanics, second edition, Oxford University Press (2000). C. B. P. Finn, Thermal Physics, second edition, Chapman & Hall (1993). A. M. Glazer and J. S. Wark, Statistical Mechanics: A Survival Guide, Oxford University Press (2002). T. Guenault, Statistical Physics, second edition, Chapman & Hall (1995). G. Morandi, E Ercolessi, and F Napoli, Statistical Mechanics: An Intermediate Course, 2nd Edition, World-Scientific (2001), M. Zemansky and R. Dittman, Heat and Thermodynamics, McGraw-Hill (1981)

Tutorials Problem sheets covering the course will be handed out as the lectures progress. 25% of the course assessment is based on solutions to tutorial questions which will be marked by tutors. A sample exam question will also be set. Assessment 2 hour examination = 75%, continuous assessment = 25%

PH3014 Transferable Skills for Physicists Semester: whole year Available: each year Credits: 15 Module co-ordinator: Dr Bruce Sinclair Overview This module allows students to practise and extend their knowledge and understanding of physics (including astronomy) at the same time as gaining important and useful experience in transferable skills. These skills, which are sometimes referred to as professional skills or key skills, are a vital part of the abilities of a graduate (astro)physicist. While many of these skills are developed in “conventional” modules, concentrating on these skills in this module should ensure that all our students have all these important abilities. These skills are vital for academic study and research, and for careers in industry, business, and elsewhere. They will help with the final year project report and presentation. Aims and Objectives We intend that this module should strengthen skills in the following areas:- • Using knowledge and solving “new” problems • Finding information from books, journals, the web, and people • Critically evaluating and interpreting information gained from the sources above • Managing your own learning • Applying initiative • Communicating orally • Communicating on paper • Working as part of a team • Using a variety of IT skills • Extending your knowledge and understanding of physics and astronomy

Learning Outcomes By the end of this module students should be able to • determine what it is that they do not yet know, but need to know in order to carry out a scientific task • use bibliographic search engines to find relevant scientific papers • use the literature and the web to find scientific information • evaluate critically information from different sources, and use this to inform a scientific argument or overview • present such an argument or overview on paper and orally • use PowerPoint appropriately to support a scientific presentation • work independently and as part of a collaborative team • know why these outcomes are important, and be confident in their ability to perform these tasks Synopsis Overview of the course and its need. The scientific literature, and associated information retrieval. Critical evaluation of material, including a student-comparison of two scientific papers. What makes a good oral presentation? Introduction to PowerPoint. The production of a short talk on one chosen-subject to a small group, followed later in the session by a 20 minute talk on a different subject at a weekend away in the Scottish Hills. Scientific writing, with the production of a 2000-word review article. Team skills, including case studies using scientific knowledge to solve particular problems. The final assignment in the module involves using all the above skills as each group develops a proposal for a new teaching lab experiment or a research project. Prerequisites Students are expected to have a general knowledge and understanding of physics appropriate with passing level two physics in this University, or equivalent. This module is compulsory for students undertaking a degree topic taught wholly within the School, and may also be taken by those doing a joint degree involving physics. Recommended books A Wilson, Handbook of Science Communication, IOPP, 1998, ISBN 0750305185 - £12 - This book is the result of an initiative of the Institute of Physics. Parts of the book have an emphasis on the public understanding of science, but there are other parts that are directly relevant to the communication skills that we are developing in this module. Well worth having your own copy for reference. M Davis, Scientific Papers and Presentations, Academic Press, 1997, ISBN 0122063708, £14.95 – This is aimed at science graduates doing research, but it contains lots of useful stuff on writing and presentations. Appendix 11 is great.

R R H Anholt, Dazzle ‘em with Style, Freeman, 1994, ISBN 0716725835, £10.95. This is a book giving clear instructions on how to prepare and present a good research presentation (paper at a conference, or seminar at a visit). However, many of these skills transfer to the sort of talks that you will be doing S Drew and R Bingham, The Student Skills Guide, Gower, 1997, ISBN 0566078473, - £12.95. This would also be a great purchase. The authors have produced what is a combination of a textbook and a workbook. There is lots of useful advice on study skills, writing, presentations, and group work, along with places to write in your answers to various structured questions. A Northedge et al, The Sciences Good Study Guide, Open University, 1997, ISBN 0749234113, - £11.99 – Aimed at early undergraduates this has a look at study techniques, taking notes, etc, before a particularly useful chapter nine on writing. Class Sessions The class meets on most Wednesdays at noon, either as a whole class or in tutorial groups of about four students each. There are also some other sessions, including the trip to the Scottish hills (often the Burn House near Edzell) for a weekend. Students complete a series of relevant assignments through the year. Assessment There is no written examination. The module is assessed on the student work generated through the year.

PH3061 Quantum Mechanics I Semester: 1 Available: each year Credits: 10 No of Lectures: 16 Lecturer: Professor Malcolm H. Dunn Overview Quantum Mechanics is that description of physical phenomena in which the wave and particle aspects of matter and radiation are reconciled in a unified theory. As such it is one of the most fundamental topics in physics. It has widespread applicability in virtually every area of physics from the solid-state to fundamental particles, and is hence an essential item in the “toolbox” of any practitioner in modern physics. As a theory it has never been shown to be incorrect in any of its predictions if properly employed. However, at a fundamental level it poses many paradoxes and challenges to our understanding, and this is an area of much current research. As well as playing a key role in describing many traditional areas of physics, deeper insights continue to emerge, leading to new applications such as quantum

computing, quantum cryptography and quantum information processing. It is hence a topic of continuing fundamental interest and study in its own right as well as being essential for describing many areas of applied physics. The present course is the first in a sequence of four courses that progressively develop the topic to an advanced level. The present course is based on the Schrödinger equation description of quantum mechanics (often referred to as wave mechanics), and is limited to non-relativistic situations. A more formal approach to describing quantum systems based on operator methods is also developed. Applications covering a range of important physical situations are considered, as well as some of the current challenges and paradoxes. Essential mathematical background is developed throughout the course. Aims & Objectives To present an introductory account of quantum mechanics (wave mechanics) including important applications and recent progress, in particular: • To develop an intuitive understanding of such basic concepts as the wave function, probability density, operators, eigenfunctions and eigenvalues. • To introduce both the time-independent and time-dependent Schrödinger equations and to develop an understanding of their meaning and how they are utilised. • To apply the Schrödinger equation(s) to a range of important physical situations, develop solutions and discuss their implication. • To introduce the operator formalism and consider a number of its applications. • To introduce and apply time-dependent perturbation theory. • To develop an insight into some of the new applications and current paradoxes in quantum mechanics. Learning Outcomes You will have acquired: • A conceptual understanding of the basis of quantum mechanics (wave mechanics). • An ability to construct the Schrödinger Wave Equation by heuristic arguments from first principles. • Techniques for solving the Schrödinger equation for a number of important situations including both in one and three dimensions. • An ability to solve time-dependent problem through the use of perturbation techniques. • An understanding of concepts such as the collapse of the wave-function, quantum jumps, quantum interference and superposition states. • An ability to apply the operator approach to problem solving. • A knowledge of a number of mathematical techniques relevant to solving wave equations. • Overall a portfolio of problem solving skills in Quantum Mechanics and an ability to apply them to new problems.

Synopsis Review of experimental evidence for the wave properties of matter - historical and contemporary. de Broglie relation. The “quantum interference experiment”, wave particle duality, superposition, collapse of the wave-function, probability density. Revision on wave equations and their solutions including the WKB method. The wave-function of quantum mechanics; why it is complex. Plane waves. Derivation of the Schrödinger Wave Equation, both time-independent and time-dependent. Propagation of wave packets; group velocity and spreading. Propagation through potential steps and barriers, tunnelling. Eigenvalues and Eigenfunctions. Particles in one dimension. Both infinite and finite, 1-D, potential wells. Expansion postulates and measurement. The Simple Harmonic Oscillator. Summary of the general structure of wave mechanics, leading to operator methods in Quantum Mechanics. Restatement in terms of postulates. Ladder operator approach to the Simple Harmonic Oscillator. Angular momentum quantisation, including raising & lowering operators. Schrödinger Equation in 3-D. The Hydrogen atom. Time-dependent perturbation theory. Rabi flopping and its relation to stimulated emission. Quantum jumps. Applications in Quantum computing and Quantum Cryptography. Paradoxes, Quantum measurements. Entanglement and EPR. Recommended Books Recommended for Purchase: S. Gasiorowicz, Quantum Physics (3rd Edition), Wiley International Editions, 2003, £37) Recommended for Consultation: R.P. Feynman, Lectures on Physics, Addison Wesley. L.D. Landau & E.M. Liftshitz, Quantum Mechanics (Course in Theoretical Physics Volume 3), Butterworth-Heinemann. S Brandt and H D Dahman, The Picture Book of Quantum Mechanics, Wiley. A Messiah, Quantum Mechanics (2 Volumes), North Holland. L I Schiff, Quantum Mechanics (2nd Edition), McGraw-Hill. E. Merzbacher, Quantum Mechanics (3rd Edition), John-Wiley, 1998. R H Dicke and J P Wittke, Introduction to Quantum Mechanics (Addison Wesley) Tutorials

Three whole class tutorials within lecture timetable. Small group tutorials, held once per week, will include a discussion of Quantum Mechanics I every second week. Assessment 2 hour examination = 75% Continuous assessment = 25% Continuous assessment will be based on submission to tutors for marking of a number of problems drawn from tutorial sheets.

PH3062 Quantum Mechanics 2 Semester: 2 Available: each year Credits: 10 Number of Lectures: 18 Lecturer: Dr C A Hooley Overview To expand students' basic knowledge gained in PH3061 Quantum Mechanics 1 particularly in approximation methods, time-dependent effects and many-particle systems. Aims and Objectives This module explores more of the main features of quantum mechanics. These include: • a review of selfadjoint operators, their eigenvalues and eigenfunctions, • quantum dynamics • superposition principle • Dirac notation and scalar product, • representation of physical observables by selfadjoint operators and the implications of commutation relations on the compatibility of observables • approximation methods for solving energy eigenvalues and eigenfunctions • many particle systems, Fermions and Bosons, factorizable and entanglement states. Learning Outcomes By the end of the module the students should acquire a good working knowledge of quantum mechanics. They should be familiar with

• the mathematical properties of selfadjoint operators, their eigenvalues and eigenfunctions, spectral theorem, Dirac notation and its manipulation, • time-dependent Schrodinger equation and its solutions in terms of stationary states, • superposition principle and the Schrodinger cat paradox, • commutation relations on the compatibility of observables particularly in relation to position, momentum, orbital angular momentum and spin, • the application of approximation methods, including variational principle and perturbation theories, • the description of fermions and bosons, factorizable and entanglement states. Synopsis A review of selfadjoint operators, their definition and properties, including their eigenvalues and eigenfunctions, and a simplified spectral theorem. Physical significance of the spectral theorem and probabilistic interpretation in quantum mechanics. The time-dependent Schrodinger equation and its solutions in terms of stationary states. Quantum states and their coherent superposition, including the Schrodinger cat paradox. Scalar product, Dirac notation and its manipulation. Representation of physical observables by selfadjoint operators and the implications of commutation relations on the compatibility of observables with illustrations using position, momentum, orbital angular momentum and spin. Approximation methods for solving energy eigenvalues and eigenfunctions, including variational method, time-independent and time-dependent perturbation theories, Many particle systems, anti-symmetrization of the wave function for Fermions and symmetrization of the wave function for Bosons, factorizable and entangled states. Prerequisites PH3061 Recommended Books F Mandl, Quantum Mechanics (Wiley 1992). Many of the books in our library also cover the contents of the course Tutorials There are four tutorial sheets and some whole class tutorials to discuss important issues. There are also small group tutorials to help individual students. Assessment

Continuous assessment=25%, 2-hour examination=75%.

PH3066 Mathematics for Physicists Semester: 1 Available each year Credits: 10 No of Lectures: 18 Lecturer: Professor Malcolm H. Dunn. Overview The course will develop important mathematical techniques that are required as necessary mathematical background for the honours physics and astronomy courses, and which thereby form part of the mathematical repertoire of a professional physicist or astronomer. New techniques not previously covered in earlier mathematics courses but necessary for gaining a proper comprehension of and an ability to solve problems in physics/astronomy will be introduced. In addition the course will also include the revision of some previously encountered material that is of particular importance. Fourier Series (as a prelude to Fourier Transforms) and Vector Calculus fall into this latter category. Aims & Objectives To supplement the mathematical background of the honours physicist/astronomer by covering those aspects of mathematics of relevance in particular to the honours courses, but which in general also form an essential part of the training of a practicing physicist/astronomer. To do this by placing the emphasis on obtaining solutions to problems in physics and its application, rather than on pursuing mathematical rigour for its own sake. To complement the formal mathematical approaches to problem solving with those based on modern symbolic computer software, such as “Mathematica”. To use worked examples and tutorial problems as a route to learning throughout. Learning Outcomes You will have acquired: • A better working knowledge and understanding of the mathematics expected in other honours physics and astronomy modules. • An improved ability to formulate problems relating to physical phenomena in mathematical language, starting from intuitive ideas. • An ability to apply a range of mathematical techniques to the solution of such problems. • An ability to discriminate between alternative methods of solution as to which is the most suitable for the task in hand.

• An appreciation of where to apply analytical techniques and where to employ symbolic computer software methods for obtaining, checking or plotting results. • A significant enhancement of your problem solving ability as a practising physicist/astronomer. Synopsis Vector calculus (Revision) Fourier series (Revision) Fourier transforms Factorial or Gamma function Dirac delta function Partial differential equations -Solution by separation of variables -Laplace’s equation & Schrodinger equation as examples Ordinary differential equations -Series solutions Legendre polynomials Spherical harmonics Hermite polynomials Recommended Books For Purchase • Essential Mathematical Methods for Physicists, H. N. Weber & G. B. Arfken, Elsevier, 2004. (£34.99) For Consultation • Mathematical Methods for Physicists, G. B. Arfken & H. N. Weber, Academic Press (now Elsevier), 5th Ed. • Advanced Engineering Mathematics, E. Kreyszig, John Wiley, 5th Ed, • Mathematics for Scientists & Engineers, H. Cohen, Prentice Hall, 1992. • Mathematical Methods in the Physical Sciences, M. L. Boas, Wiley, 3rd Ed. • Mathematical Methods of Physics, J. Mathews & R. L. Walker, Addison Wesley (also Benjamin), 2nd Ed. • Mathematical Physics: Applied Mathematics for Scientists & Engineers, B. Kusse & E. Westig, Wiley. • Methods of Mathematical Physics, R. Courant & D. Hilbert, Interscience (2 vols). • The Mathematics of Physics & Chemistry, H. Margenau & G. M. Murphy, Van Nostrand. Tutorials Two whole-class revision tutorials within lecture timetable. In addition small group tutorials, held once per week, will include a discussion of topics in this module every second week.

Assessment 2-hour examination = 75%, continuous assessment = 25%

PH3073 Lagrangian and Hamiltonian Dynamics Semester: 2 Available: each year Credits: 10 Number of lectures: 18 Lecturer: Prof U Leonhardt Overview Traditionally, classical mechanics describes the motion of physical objects that can be modelled as point particles, such as falling stones, flying bullets or the planets orbiting the Sun or other stars. However, the concepts of classical mechanics are much more general: Mechanical particles obey the Principle of Least Action, a principle that governs the behaviour of many other objects and that can also be applied to numerous “non-mechanical” systems, for example to light rays, electronic circuits or financial markets. Furthermore, Classical Mechanics is an important ingredient of Quantum Mechanics and Theoretical Optics and it serves as the foundation of Classical and Quantum Field Theory. Aims and Objectives To give students a solid grounding and sufficient training in Lagrangian and Hamiltonian techniques in classical mechanics and their applications, including • the Principle of Least Action as the starting point of Lagrangian mechanics, • traditional applications of Lagrangian mechanics such as mechanical pendulums, planetary motion, collisions and some non-traditional ones • appreciating the problem-solving power, generality and elegance of Lagrangian and Hamiltonian techniques, • the fundamental connection between symmetries and conservation laws (Noether theorem), • Hamilton-Jacobi theory, Hamiltonian mechanics, canonical transformations, Liouville’s theorem. Learning Outcomes By the end of the module, students will have a solid knowledge of the central concepts of Classical Mechanics and will have acquired and trained important problem-solving skills. They will be able to

• establish the Lagrangian, and to derive and solve the equations of motions for many systems subject to the Principle of Least Action • appreciate the problem-solving power, generality and elegance of Lagrangian and Hamiltonian techniques • understand the connection between symmetries and conservation laws • calculate conserved quantities from symmetries • calculate the Hamiltonian and establish the Hamilton equations • be familiar with canonical transformations and Hamilton-Jacobi theory • understand the concept of phase space and the conservation of phase-space density (Liouville’s theorem) Synopsis 1. Review of Newtonian mechanics. 2. Equations of Motion: The Principle of least action. The Euler-Lagrange equations. Free and interacting particles in non-relativistic mechanics. Introductory examples to illustrate the abstract concepts that follow in sections 2 and 3. 3. Conservation Laws: Energy, momentum, angular momentum, centre of mass. The Noether theorem. 4. Canonical formalism: Hamilton-Jacobi theory. Hamiltonian techniques. Canonical transformations. Liouville theorem. 5. Applications: Two-body problem. Kepler problem (planetary motion). Collisions. Non-mechanical applications (light rays, electronic circuits). Prerequisites PH2011 (Physics 2A), MT2001 (Mathematics) and a knowledge of vector calculus. Recommended book The principal book is Mechanics by L D Landau and E M Lifshitz (Pergamon, Oxford, 1976), probably the best book in Theoretical Physics ever written. The course closely follows the central chapters of the book, complemented by some additional examples and homework problems.

Tutorials and homework Each week the students will receive sheets with about 10 short questions on the course content, to guide their understanding of the material, and a series of homework problems, to develop their skills. At least three whole class tutorials will be held to discuss these and other more general issues. The questions and homework problems will be marked. Assessment: 2-hour examination = 75% The marked homework represents a continuous-assessment component = 25%

PH3074 Electronics Information not yet available

PH3075 Applied Vector Calculus Semester: 1 Available: each year Credits: 5 Number of lectures: 9 Lecturer: Dr J Betouras Overview Vector Calculus is a branch of mathematics with which all students of physics and astronomy must become familiar. It is one of the physicist’s tools of the trade, and is particularly necessary for an understanding at honours level of electromagnetism (Maxwell’s equations) and quantum mechanics (Schrodinger’s equation). For those who have not taken the module MT2003 Applied Mathematics, this module is essential. Aims and Objectives The aim is to provide a basic grounding in vector calculus so that students acquire a knowledge of the definitions of the grad, div, curl and Laplacian operators, their application to physics, and the form which they take in particular coordinate systems. Learning Outcomes

By the end of the module, students will have a good grasp of the topics covered in the lectures and will • be able to evaluate the gradient of a scalar function and the effects of the div and curl operators on a vector function • appreciate the usefulness of, and be able to apply, the theorems of Gauss and Stokes • be able to state the form of the operators grad, div, curl and the Laplacian in Cartesian coordinates and be familiar with their form in spherical polar and cylindrical coordinates • understand and appreciate the use of vector calculus in quantum mechanics and electromagnetism. Synopsis Revision of fields and potentials. The vector operator del. The operators div, grad and curl, and their physical interpretation. Line, surface and volume integrals. The theorems of Gauss and Stokes. Curvilinear coordinates. Formulae for grad, div , curl and the Laplacian in spherical and cylindrical coordinates. Prerequisites There are no prerequisites other than an elementary knowledge of vectors, particularly the notion of scalar and vector products. Antirequisites MT2003 Applied Mathematics Tutorials There will be two whole class tutorials to discuss general issues and resolve any problems. Assessment: Continuous assessment via exercises and tests = 100%

PH3101 Physics laboratory 1 Semester: 2 Available: each year.

Credits: 15 No. of Sessions: 21 afternoon sessions of three and a half hours each. Module Co-ordinator: Professor Malcolm H. Dunn Overview This module is made up of a set of sub-modules, each one lasting for four afternoon sessions with students undertaking five sub-modules in the course of the semester. Sub-modules presently on offer include: Lasers, X-ray Crystallography, Electronics, Phase Transitions in Nickel Powders, LabView, and Towards the Quantum Limit. These may change, for example as new experiments are introduced. Descriptions of the present sub-modules are given below.

The class is divided into self-selected groups, usually of eight persons, which then circulate around the sub-modules sequentially.

The structure of the sub-modules differs from one to another. In some, students work on the same set of experiments, usually in pairs. In others, there are a number of experiments based around a common theme; following an introductory overview, students work singly or in pairs on specific experiments. Some of the sub-modules conclude with feedback sessions where students present the outcomes of their experimental work to their peers and demonstrators, followed by discussion. Other sub-modules aim at building basic skills such as in electronics or computer-based data handling. All the experiments are up-to-date and relevant to the training of a practising physicist, with a number of the experiments closely related to those found in contemporary research laboratories. The variety of approaches offered ensures that you will find this laboratory both enjoyable and stimulating.

The first session is taken by the class as a whole and includes an important safety seminar, covering electrical, chemical, cryogenic and laser safety, followed by practical advice on the keeping of laboratory note-books, etc.

Aims & Objectives

• To give you practical experience of some pervasive experimental techniques relevant to a practising physicist, e.g. electronic design, computer-based data handling, optical spectroscopy, x-ray crystallography.

• To introduce you to important contemporary developments in experimental physics, e.g. scanning tunnelling microscopy, lasers and nonlinear optical devices, optical and electromagnetic traps.

• To strengthen your understanding of important physical concepts, e.g. phase transitions, quantum interference, atomic scattering, quantum tunnelling.

• To develop sound practice in a number of important generic skills such as planning of experiments, risk assessment, record keeping, data handling and evaluation, error analysis, drawing evidence-based conclusions, identifying future work.

• To enhance manual and mental dexterity at performing experiments. • To develop transferable skills with regard to the presentation of research outcomes

through both written work and oral presentations.

• To gain experience of carrying out experimental work while working alone, in partnership, and in small groups.

Learning Outcomes You will have acquired:

• familiarity with a range of important and pervasive experimental techniques, • practical experience of contemporary experimental equipment, including some used in

present-day research laboratories, • a fuller understanding of a range of important physical concepts through exploring

them in experimental situations, • key generic skills required by an experimentalist in the physical sciences,

encompassing documentation, assessment, deduction, and presentation, • ability to work both on your own and collaboratively.

Synopsis

Phase Transitions in Nickel Powders (PT) The experiment is to investigate the dynamics and cooperative effects of a fine ferromagnetic powder when agitated by electric and/or magnetic fields. A team of four will be expected to divide up the tasks needed to understand the electrostatic and magnetic forces involved in moving the grains; investigate the appropriateness of the design of the cell containing the powder and the coils for producing the magnetic field and of interfacing a video camera and instrumentation using LabView. The cooperative effects between the grains depend on the level of excitation in a way that loosely corresponds to phase transitions as a function of temperature. Success would be a 'phase diagram' for the system.

LabView (LV)

LabVIEW is an industry-standard programming and control environment. It is used throughout science and engineering as a means of creating programs, and is ubiquitous in laboratories that require instrument control. A familiarity with LabVIEW is therefore a very saleable transferable skill. The purpose of this sub-module is to give the student an introduction to programming and the use of LabVIEW. By the end of this sub-module the student should be able to build a LabVIEW virtual instrument (VI) to undertake a specified task. The sub-module develops the student through finding out about the LabVIEW environment, ensuring they become familiar with the various windows, menus and tools. Next a simple VI is created, edited and debugged. The use of sub-VIs is discussed and two means of creating these undertaken; including setting up an icon and connector pane. Loops, program structures, arrays, charts and graphs are also introduced and used in the development of various VIs. The lab culminates in using LabVIEW’s control ability to interrogate a GPIB instrument simulator. The student learns how to communicate with a GPIB instrument, and puts into practice some of their newfound skills in interpreting and visualising simulated experimental measurements. At the end of these four afternoons the student will have the skill needed to start using LabVIEW to tackle future projects. Lasers (L)

In the first half of the sub-module the group will be working together investigating aspects of the longitudinal and transverse modes of lasers. This will allow students to explore important aspects of laser physics that also tie in with ideas in quantum mechanics and in oscillations and waves. The activities also develop aspects of experimental technique and the interpretation of the science behind various observations. In the second pair of afternoons students will work individually on their choice of one of a number of laser experiments. These may include various laser systems, conversion of laser light from one frequency to another, fibre optics, holography, remote sensing of speed with lasers, and the optics of optical data storage.

Electronics (E)

An understanding of the basic principles of electronics is invaluable in the physics research laboratory. Whilst many designs are constructed and tested on the bench in a trial and error fashion, it is often highly desirable to be able to model the behaviour of a circuit on a computer to aid component value selection and hone its characteristics. Of particular interest in experimental research is the design and application of filters, which use capacitors, inductors, resistors or a combination of these. It is often difficult to diagnose the characteristics of these circuits on the very short (transient) time scale, and so computer modelling becomes very important. In this module you will be introduced to such a modelling program, 'Microcap IV', and use it to investigate various simple circuits in the transient and steady-state regime to get a feel for how they react.

Towards the Quantum Limit (QL) The invention of such devices as the scanning tunnelling microscope and the development of various methods of trapping particles either electromagnetically (e.g. Paul Trap) or optically (e.g. Optical Tweezers) has taken physics to the quantum limit of “seeing” entities such as individual atoms or molecules. The two-slit interference experiment when conducted with only single photons in the apparatus at any one time is another example of observation taken to the quantum limit. These are the experiments that you will encounter in this sub-module. Following an overview of the experiments during the first afternoon, the group will break up into four pairs with each pair carrying out one of the four experiments over the next two afternoons. The final afternoon will be the feedback session in which students, in pairs, will discuss the perspective of their experiment, elucidate its conceptual foundations, present and evaluate their results, and reach conclusions for further discussion by the group as a whole; very much along the lines of presenting an invited paper at a conference. X-ray Crystallography (X) X-Ray crystallography is among the most important methods for identifying the atomic lattice structure of synthesized crystalline materials and is commonly employed in everyday research in this university. Thanks to a recent major investment in this Junior Honours experiment, you now have the chance to work with the most modern, computer controlled x-ray diffractometer available for undergraduate teaching. On the first day of the experiment you will concentrate on becoming familiar with the experimental apparatus and the fundamental techniques in x-ray crystallography such as Laue and Debye-Scherrer diffraction as well as how to analyse the data that you obtain. However, the main focus will be the second part of the lab, which is much closer to real life research. The task here is to use the methods you have learned to analyse an unknown substance and determine its lattice structure as well as inter atomic spacings. On the last day the groups will then present their findings in a short presentation followed by a discussion. Overall this laboratory aims at creating the opportunity for you to experience part of the everyday detective work one is confronted with in condensed matter physics research

Pre-requisites The only requirement is entry into the JH class. Recommended Books and Other Literature No book is recommended covering the whole of this module. For each sub-module students will receive handouts providing a general introduction, including references to review articles and other recommended reading material. Additional documentation provides more detailed information required for the experiment. Students are encouraged to carry out literature searches appropriate to the experimental work they are undertaking. Laboratory Notebook It is important that students keep up-to-date and properly laid out lab books. Advice on this will be given at the first session. Assessment Assessment for each sub-module involves marking of the experimental work (around 70%), along with a test or presentation (around 30%). Assessment procedures differ from topic to topic, and demonstrators will advise on particular arrangements for each topic. All topics are weighted equally in the calculation of the final mark and grade. Full Report Over the period of the Easter vacation, students are required to write up a full report on one of the experiments that they have carried out. The mark for the Full Report is included in the final assessment and hence final grade awarded.

PH3110 Physics Laboratory Semester: whole year Available: each year. Credits: 15 Module Co-ordinator: Professor Malcolm H. Dunn Overview This module is made up five sub-modules, each one lasting for four afternoon sessions. These currently comprise: Lasers, Optics and Spectroscopy, Towards the Quantum Limit, Phase Transitions in Nickel Powders, and the software package LabView.

The structure of the sub-modules differs from one to another. In some, students work on the same set of experiments, usually in pairs. In others, there are a number of experiments based around a common theme; following an introductory overview, students work singly or in pairs on specific experiments. Some of the sub-modules conclude with feedback sessions where students present the outcomes of their experimental work to their peers and demonstrators, followed by discussion. All the experiments are up-to-date and relevant to the training of a practising physicist, with a number of the experiments closely related to those found in contemporary research laboratories. The variety of approaches offered ensures that you will find this laboratory both enjoyable and stimulating.

The first session is taken by the class as a whole and includes an important safety seminar, covering electrical, chemical, cryogenic and laser safety, followed by practical advice on the keeping of laboratory note-books, etc.

Aims & Objectives

• To give you practical experience of some pervasive experimental techniques relevant to a practising physicist.

• To introduce you to important contemporary developments in experimental physics. • To strengthen your understanding of important physical concepts. • To develop sound practice in a number of important generic skills such as planning of

experiments, risk assessment, record keeping, data handling and evaluation, error analysis, drawing evidence-based conclusions, identifying future work.

• To enhance manual and mental dexterity at performing experiments. • To develop transferable skills with regard to the presentation of research outcomes

through both written work and oral presentations. • To gain experience of carrying out experimental work while working alone, in

partnership, and in small groups. Learning Outcomes You will have acquired:

• familiarity with a range of important and pervasive experimental techniques, • practical experience of contemporary experimental equipment, including some used in

present-day research laboratories, • a fuller understanding of a range of important physical concepts through exploring

them in experimental situations, • key generic skills required by an experimentalist in the physical sciences,

encompassing documentation, assessment, deduction, and presentation, • ability to work both on your own and collaboratively.

Synopsis

Lasers (L)

In the first half of the sub-module the group will be working together investigating aspects of the longitudinal and transverse modes of lasers. This will allow students to explore important

aspects of laser physics that also tie in with ideas in quantum mechanics and in oscillations and waves. The activities also develop aspects of experimental technique and the interpretation of the science behind various observations. In the second pair of afternoons students will work individually on their choice of one of a number of laser experiments. These may include various laser systems, conversion of laser light from one frequency to another, fibre optics, holography, remote sensing of speed with lasers, and the optics of optical data storage.

Optics and Spectroscopy This aims to give practical experience of important techniques in modern optics, particularly in spectroscopy. The first three afternoons are spent on work in pairs and small groups involving spectroscopy with prisms, gratings, Fabry-Perot interferometers, and a Fourier transform spectrometer. One experiment measures the splitting of spectral lines in neon in a magnetic field. A tunable coherent optical source is demonstrated. The final two afternoons are spent on an experiment of the student's choice in the area of optics and spectroscopy. These aim to develop experimental planning and design skills as well as the investigation techniques and exploring of science that are practised in the first three afternoons.

Phase Transitions in Nickel Powders (PT) The experiment is to investigate the dynamics and cooperative effects of a fine ferromagnetic powder when agitated by electric and/or magnetic fields. A team of four will be expected to divide up the tasks needed to understand the electrostatic and magnetic forces involved in moving the grains; investigate the appropriateness of the design of the cell containing the powder and the coils for producing the magnetic field and of interfacing a video camera and instrumentation using LabView. The cooperative effects between the grains depend on the level of excitation in a way that loosely corresponds to phase transitions as a function of temperature. Success would be a 'phase diagram' for the system.

LabView (LV)

LabVIEW is an industry-standard programming and control environment. It is used throughout science and engineering as a means of creating programs, and is ubiquitous in laboratories that require instrument control. A familiarity with LabVIEW is therefore a very saleable transferable skill. The purpose of this sub-module is to give the student an introduction to programming and the use of LabVIEW. By the end of this sub-module the student should be able to build a LabVIEW virtual instrument (VI) to undertake a specified task. The sub-module develops the student through finding out about the LabVIEW environment, ensuring they become familiar with the various windows, menus and tools. Next a simple VI is created, edited and debugged. The use of sub-VIs is discussed and two means of creating these undertaken; including setting up an icon and connector pane. Loops, program structures, arrays, charts and graphs are also introduced and used in the development of various VIs. The lab culminates in using LabVIEW’s control ability to interrogate a GPIB instrument simulator. The student learns how to communicate with a GPIB instrument, and puts into practice some of their newfound skills in interpreting and visualising simulated experimental measurements. At the end of these four afternoons the student will have the skill needed to start using LabVIEW to tackle future projects. Towards the Quantum Limit (QL) The invention of such devices as the scanning tunnelling microscope and the development of

various methods of trapping particles either electromagnetically (e.g. Paul Trap) or optically (e.g. Optical Tweezers) has taken physics to the quantum limit of "seeing" entities such as individual atoms or molecules and hence being able to probe the ways in which they interact. The two-slit interference experiment when conducted with only a single photon in the apparatus at any one time is another example of observation taken to the quantum limit, and probes what Richard Feynman called the "only mystery of quantum mechanics". . These are the experiments that you will encounter in this sub-module. Following an overview of the experiments during the first afternoon, the group will divide into four pairs with each pair carrying out one of the four experiments over the next two afternoons. The final afternoon will be the feedback session in which students, in pairs, will discuss the perspective of their experiment, elucidate its conceptual foundations, present and evaluate their results, and reach conclusions for further discussion by the group as a whole, very much along the lines of presenting an invited paper at a conference. Pre-requisites Entry to the JH class in Microelectronics and Photonics Recommended Books and Other Literature No book is recommended covering the whole of this module. For each sub-module students will receive handouts providing a general introduction, including references to review articles and other recommended reading material. Additional documentation provides more detailed information required for the experiment. Students are encouraged to carry out literature searches appropriate to the experimental work they are undertaking. Laboratory Notebook It is important that students keep up-to-date and properly laid out lab books. Advice on this will be given at the first session. Assessment Assessment for each sub-module involves marking of the experimental work (around 70%), along with a test or presentation (around 30%). Assessment procedures differ from topic to topic, and demonstrators will advise on particular arrangements for each topic. All topics are weighted equally in the calculation of the final mark and grade. Full Report Students are required to write up a full report on one of the experiments that they have carried out. The mark for the full report is included in the final assessment and hence final grade awarded.

PH4021 Physics of Atoms Semester: 1 Available: each year Credits: 15 Number of lectures: 27 Lecturer: Dr D Cassettari Overview Probing and understanding the structure of atoms is central to many areas of science and even within many studies in astrophysics. Atomic physics itself has undergone a revolution in the last twenty years and is now a “hot” topic in physics. This module aims to enhance our understanding of the internal structure of atoms and understanding of atomic interactions with magnetic and electric fields. We will extend this knowledge by applying it to effects in multi-level systems and recent advances such as laser cooling and Bose-Einstein condensation (topics of Nobel Prizes in 1997 and 2001). Learning outcomes Students will acquire a detailed understanding of internal structure of atoms, the influence of magnetic and electric fields on atomic spectra, a knowledge of hydrogen, helium and alkali spectra, laser cooling in practice, optical techniques for probing atoms, developing a Bose-Einstein condensate, and the difference between bosons and fermions . Students will be able to investigate details of given atomic structures, be able to calculate effects of external magnetic and electric fields, understand and know how to implement laser cooling experimentally and develop a Bose Einstein condensate Synopsis The course will start by recapping on the revolution in physicists’ understanding at the beginning of the 20th century that led to the nuclear model of the atom. Then we will progress to understanding the structure of hydrogen in greater depth looking at radial and angular wavefunctions. Alkali atoms and screening will be discussed. The course then progresses to topics such as electron spin, the Stern-Gerlach experiment, spin-orbit coupling, fine structure, Lamb shift, electron spin resonance, Zeeman effect, optical pumping, Stark effect, and the helium atom. The concluding part of the course will discuss laser cooling and Bose-Einstein condensation (BEC) explaining basic laser cooling, Doppler theory, sub Doppler cooling, magneto-optical traps, evaporative cooling, magnetic trapping , signatures of BEC and Fermi gases.

Recommended books Haken and Wolf, The Physics of Atoms, sixth edition, Springer Verlag Thorne, Spectrophysics: principles and applications, Springer-Verlag Harold J. Metcalf and Peter van der Straten, Laser cooling and trapping, Springer Verlag (only for last five lectures but good reference – not for purchase as we have two in the library) Assessment 2-hour examination = 100%

PH4022 Nuclear and Particle Physics Semester: 2 Available: each year Credits: 10 Number of lectures: 18 Lecturer: Dr N C McGill Overview Nuclear physics is concerned with the structure and composition of atomic nuclei, and the various theories which have proposed to account for their observed properties. No one theoretical model is found to be wholly satisfactory, and nuclear theory is a patchwork of mutually inconsistent models valid only in certain circumstances and for certain purposes. In contrast, particle physics aims to give a coherent description of the basic building blocks of matter (quarks and leptons), the composite particles which can be constructed from them, the fundamental forces which act on them, and the mechanism by which these forces are transmitted. Aims and Objectives To present an introductory account of nuclear physics and fundamental particles, including • observational aspects of nuclei, including their size, spin and parity properties, and binding energy • nuclear models – Fermi gas, liquid drop and shell models • the semi-empirical mass formula, and deductions from it concerning nuclear stability • the theory of alpha-decay • the classification of fundamental particles and their interactions according to the standard model

• quark structure of the composite meson and baryon families of particles. Learning Outcomes By the end of the module, students will have a comprehensive knowledge of the topics covered in the lectures and will be able to • determine binding energies from the masses of nuclides, • state what is meant by the independent particle assumption, • explain the term “spin-parity state” of a nuclide, • explain the origin of the terms in the semi-empirical mass formula, • derive the analytical form of the stability line for nuclei • relate the half-life to alpha-particle energy, for nuclei which suffer alpha-decay • make predictions regarding the mode of decay of unstable hadrons • explain the reason why colour charge is attributed to quarks. Synopsis History of the subject, definitions. The nuclear atom. Nuclear size and binding energy. Mass excess. Quantum mechanics applied to the nucleus. The independent particle model. QM analysis of the deuteron. Angular momentum, magnetic moments of nuclei. Spin and parity. Characteristics of the strong force. Tensor force character of the strong force. Charge symmetry and charge independence. Radioactivity. Branched and sequential decays. Models - Fermi gas, liquid drop. The semi-empirical mass formula. Application to neutron stars. The shell model and spin-orbit coupling. Stability of nuclei against beta-decay.. The stability line and drip lines. Alpha -decay and quantum mechanical tunnelling. Classification of fundamental particles. Fundamental forces and their ranges.

The Dirac equation and anti-particles. Feynman diagrams. Leptons, and lepton quantum numbers. Quarks, baryons and mesons. Conservation (or otherwise) of quark quantum numbers. Accelerators. The significance of colliding beam accelerators. Parity violation in beta-decay. Isospin and resonances. Hypercharge and colour charge. Prerequisites There are no prerequisites other than a basic knowledge of quantum mechanics - which students will have obtained in PH3061, and an elementary knowledge of the special theory of relativity. Recommended books Introductory Nuclear Physics by K S Krane (Wiley 1988) Very comprehensive but contains perhaps too much detail. Nuclear Physics: Energy and Matter by J M Pearson. (Adam Hilger 1986) More readable but sometimes does not give enough detail. Particle Physics by B R Martin and G Shaw (Wiley 1997) Only the first few chapters are covered in this module. An Introduction to the Physics of Nuclei and Particles by R A Dunlap (Thomson 2003) Perhaps has the best correspondence with the lectures; but leaves out considerable detail in order to cover so much ground in so a slim volume Tutorials There will be three problem sheets, and at least two whole class tutorials will be held to discuss these and other more general issues. A sample examination question will be given out and answers will be expected to be handed in by a due date for marking and return. Assessment: 2-hour examination = 100% There is no continuous assessment in this module

PH4025 Physics of Electronic Devices Semester: 2 Available: each year Credits: 15 Number of lectures: 27 Lecturer: Dr G A Turnbull Overview Materials with electronic band gaps of up to ~3 eV, and resistivities in the range typically 10-3 to 109 Ωm, are known as semiconductors. Their electronic properties are strongly temperature dependent, and may be readily manipulated through the controlled addition of dopants. Through an understanding of the physics of semiconductors, it is possible to create designer electronic materials with a wide range of properties. Junctions between differently doped semiconductors can be readily fabricated, which form the basis of simple electronic components that underpin all modern solid-state electronics. Aims and Objectives The course describes the physical phenomena involved in the operation of semiconductor devices, and then shows how the phenomena determine the properties of specific devices such as transistors, light emitting diodes and semiconductor lasers. Synopsis Semiconductor properties: band-gaps, optical and electrical properties Conduction in an electric field and by diffusion Factors determining the concentration of electrons and holes The continuity equation Properties of pn junctions and Shottky diodes Typical devices: bipolar transistor, field effect transistor, MOSFET, light-emitting diodes, semiconductor lasers Recommended books Donald A Neamen, Semiconductor Physics and Devices (2nd Ed) (Irwin) B Tuck and C Christopoulos, Physical Electronics (Edward Arnold) D A Fraser, The Physics of Semiconductor Devices (4th Ed) (OUP) D H Navon, Semiconductor Microdevices and Materials (Holt, Rinehart and Winston) Tutorials There will be a series of tutorial sheets, and at least three whole class tutorials will be held to discuss these and other more general issues.

Assessment: 2-hour examination = 100% There is no continuous assessment in this module.

PH4026 Radio and Coherent Techniques Information not yet available

PH4027 Optoelectronics and Nonlinear Optics 1 Semester: 1 Available: Each year Credits: 15 Number of lectures: 27 Lecturers: Dr M McDonald, Prof I D W Samuel and Prof T F Krauss Overview Optoelectronics is generally understood as the union of electronics and optics. Optoelectronics is mainly concerned with the generation, manipulation and detection of light in electronic materials. These materials are typically semiconductors, e.g. silicon and gallium arsenide, but can also be more exotic such as liquid crystals and organic semiconductors. Optoelectronics is all-pervasive and covers a large number of everyday applications, ranging from the ubiquitous LED, televisions and computer displays, as well as lasers in CD players, to sophisticated equipment for high-speed telecommunications applications that form the backbone of the internet. While classical optics is concerned with linear interactions of light and matter, such as refraction, nonlinear optics deals with light-matter interactions that usually occur at higher powers, i.e. strong electromagnetic fields. Typically, the incident field is so strong that the material can no longer respond linearly. This leads to fascinating effects such as second harmonic generation (often used to generate green and blue light from an infrared source), optical bistability and self-focussing. Aims and Objectives The aim of the module is to introduce students to the basic physics underpinning optoelectronics and nonlinear optics, and to provide them with a perspective of contemporary developments in the two fields. This gives opportunities for recognising physics in action in the real world, as experienced by a range of consumer goods used in everyday life. Learning Outcomes

Students will: • gain an appreciation for the wide range of optoelectronic principles and devices used in everyday life. • understand the working principles of display devices, appreciate the differences and limitations of different technologies. • understand how electric fields can control the orientation of liquid crystals and the resulting impact on the propagation of polarised light through the medium. • realise the operation and potential of organic light emitters. • understand the principles of confining light in optical waveguides and fibres. • be able to design different types of optical waveguides. • understand fibre optics and the basics of optical telecommunications. • experience the working principles of light detectors and modulators and where they are used. • understand the principles of linear and non-linear light-matter interactions. • understand the difference between passive and dynamic non-linear optics. Appreciate the potential and limitations of nonlinear optics. Synopsis The module starts with an overview of optoelectronic devices and systems, then covers the areas of displays, detectors and modulators, optical waveguides, fibre optics and nonlinear optics. Displays: Photoluminescence and electroluminescence. Semiconducting polymers. Factors determining efficiency. Light emitting diodes and FETs. Liquid crystals and their different phases. Operation of liquid crystal displays. Optical waveguides: Waveguiding principle. Derivation of waveguide parameters. Waveguide bends. Loss mechanisms and limitations. Practical applications of optical waveguides. Introduction to planar waveguide circuits (PLCs) and use in photonic systems. Optical fibres and fibre amplifiers. Modulators and detectors: Detection mechanism. Sources of noise, state-of-the-art performance and limitations. Principles used in optical modulation. Materials used in modulators. Nonlinear optics: Introduction to nonlinear effects. Second order nonlinear optics. Harmonic generation. Sum-frequency mixing. Phase matching and optical parametric oscillators. Third

order nonlinear effects. Dynamical non-linearity, non-linear absorption and optical bistability. Nonlinear refractive index. Self-phase modulation, self-focussing, four-wave mixing. Prerequisites The course assumes a basic understanding of electromagnetism, as provided by either PH3064/PH3065 or PH3007. Recommended books A. Yariv, Optical Electronics in Modern Communications, Oxford University Press Wilson and Hawkes Optoelectronics: an Introduction (Not as heavy as Yariv, a little friendlier) Collings and Hird, Introduction to Liquid Crystals (Taylor Francis, London) Yeh and Gu, Optics of Liquid Crystal Displays, (Wiley) Assessment There will be a 2-hour examination counting for 100 % of the mark.

PH4028 Quantum Mechanics 3 Semester: 2 Available: each year Credits: 10 Number of lectures: 18 Lecturer: Dr N Korolkova Overview This module presents more advanced topics in quantum mechanics, starting with the representation of dynamical variables by operators and matrices and ending with the most topical issues of quantum information processing. Aims and Objectives The core idea of the course is to give a clear picture of the modern, 21st century quantum mechanics and to teach basic operational tools in this context. • In the first part, students are introduced to matrix mechanics as a convenient formalism in applications of operator methods and to the notion of the density matrix as the most general state description. • In the second part basic notions and main problems in the quantum theory of scattering are presented. Its modern applications in understanding the behaviour of

quantum degenerate gases will be briefly discussed (Bose-Einstein condensates and degenerate fermionic gases). • The third part of the course will introduce the main quantum information concepts such as quantum entanglement; quantum bits (qubits); quantum teleportation and quantum key distribution. Learning Outcomes By the end of the module, students will have a comprehensive knowledge of the topics covered in the lectures and will be able to • perform calculations using matrix representation of the quantum-mechanical operators using the toolbox of linear algebra , • use density matrix of a quantum state for its characterisation, operate with both mixed and pure quantum states and determine the purity of the state, • use Heisenberg, Schrodinger and interaction pictures to describe time evolution of quantum states, • formulate the quantum scattering problem, • use the Born approximation and partial wave decomposition to calculate the scattering cross-section and/or scattering amplitude, • understand basic physics behind a special type of matter, i.e.quantum degenerate gases, • understand the notion of quantum entanglement, • understand sample problems in quantum information, for example, be able to demonstrate via simple calculations in Dirac notation how quantum teleportation works. Synopsis Review of the basic postulates and the representation of dynamical variables by operators. Matrix representation of the operators. Density matrix. Purity of the state. Time evolution in quantum mechanics: Heisenberg, Schrodinger and interaction picture. Scattering problem in quantum theory. Scattering cross-section and scattering amplitude. Born approximation in quantum scattering theory. Partial wave decomposition in quantum scattering theory. Potential barrier. Optical theorem.

Brief introduction into application of the quantum scattering theory to ultra-cold quantum gases. Bose-Einstein condensation. Quantum degenerate gases with Fermi-Dirac statistics. Quantum information processing – what is it all about? Quantum bit (qubit). Quantum entanglement. Definitions, some basic measures, applications. Quantum teleportation. The Bennett protocol. Quantum key distribution. The BB84 protocol. Prerequisites PH3061, PH3062 Recommended books For the first two parts of the course the principal books are Quantum Mechanics by E. Merzbacher and Quantum Mechanics, Volume 1, by A. Messiah. For some issues of the scattering theory and of the matrix representation Quantum Mechanics by L. I. Schiff might be very useful. Some problems of scattering theory are well explained in Quantum Mechanics by Gottfried. For the third part of the course Physics of Quantum Information (ed. D. Bouwmeester, A. Ekert, A. Zeilinger) and Quantum Computation and Quantum Information by M. Nielsen and I. Chuang may be used, the latter book is more mathematical and rigorous. Tutorials There will be several problem sheets, and at least three whole class tutorials will be held to discuss these and other more general issues. Sample examination questions will be given out and answers will be expected to be handed in by a due date for marking and return. Assessment: 2-hour examination = 100% There is no continuous assessment in this module

PH4030 Computational Physics Semester: 2 Available: each year Credits: 10 Number of teaching labs (2.5 hrs): 13-14 Number of (optional) project labs: 4-6 Lecturers: Dr A Gillies and Dr M Mazilu

Overview Advanced mathematical computational tools are increasingly a common feature in both academic and industrial research labs. These are used both for rapid problem solving to aid research and for more complex modelling of physical phenomena. A number of advanced commercial programs are available including Mathematica, Maple, Matlab and MathCAD. Mathematica is one of the more advanced and easier programs to use and is currently the most common mathematical computational tool used in both experimental and theoretical research in physics at St Andrews. Research groups increasingly value knowledge of such programs. This course is designed to provide students with the skills required to tackle and solve complex physical problems using Mathematica. Aims and Objectives To develop a level of expertise in Mathematica and to introduce various common techniques used to solve and visualise physical problems, including: 2-D and 3-D graphical output including movies for visualisation of physics problems Use of Fourier transforms and 2-D Fourier transforms e.g. for image manipulation Use and application of matrix manipulation Solution of first and second order differential equations Use of compile to speed up computationally intensive procedures Introduction to symbolic programming Learning Outcomes The students will be able to program in Mathematica and be able to use Mathematica to solve, visualise and gain insight into a variety of physical problems. They should also be aware of the advanced capabilities of Mathematica including symbolic equation solving. Synopsis There are 7-8 introductory programming labs teaching basic programming skills in Mathematica. There are 6 case study labs, which are designed to provide case studies illustrating the use of Mathematica to solve and visualise a variety of Physics problems as well as introducing a number of advanced features in Mathematica. The case studies can vary from year to year but past case studies have included: Solving differential equations Fourier transforms for image processing Chaos and the Mandelbrot Set

Mechanics and motion of coupled bodies moving in a potential Analysis of periodic structures Matrix manipulation The final two to three weeks is reserved for project work. There are 4-6 (supervised) lab sessions for project work where lecturers will be available for consultation. Prerequisites There are no prerequisites and no previous knowledge of computing is required. Recommended Books The Mathematica Book by Stephen Wolfram supports the course, although this is not a required text. A large number are available on short loan from the library and the book itself is incorporated within the Mathematica program, which also features an extensive help menu. The program is available in the PC classroom. There is also now a large literature on physics problem solving using Mathematica. Assessment 30% of the final mark will be continuous assessment based on short problems or tests largely given during the teaching labs. 70% of the final mark will be based on a project where both program and report are written in Mathematica. The project will be assessed on both the written report and an oral exam, which takes the form of an informal presentation.

PH4031 Fluids Semester: 1 Available: each year Credits: 15 Number of lectures: 27 Lecturer: Dr. M M Jardine Overview Fluid dynamics is the study of all things that 'flow', whether they are liquids or gases. The underlying concepts and techniques used in this study are of wide ranging use, finding application in such diverse problems as the collision of galaxies, spacecraft re-entry into the Earth's atmosphere, or the structure and stability of fusion plasmas. Closer to home, the behaviour of fluid flows can readily be observed in rivers, on shorelines and in cloud formations. Fluid mechanics describes the types of flows that result from different forces (such as gravity). It explains how (and why) flows become supersonic and when they may become unstable. These basic principles can then be applied to a variety of problems.

Aims and Objectives • To present an introduction to fluid dynamics, focussing particularly on the underlying physics including the use of conservation relations (mass, momentum, energy) to describe flows • a physical understanding of vorticity and its evolution in a flow • the role of viscosity and its effect on flows at boundaries • the use of conservation relations to describe the behaviour of fluids at a shock • the onset of simple instabilities Learning Outcomes By the end of the module students will have an understanding of the physics of fluid flow as presented in the lectures and will be able to • apply conservation relations to determine the properties of given flow patterns • determine the vorticity of a flow and describe its behaviour • use Bernoulli's equation to analyse simple flows • describe the role of viscosity and solve for simple ideal fluid flows • use the shock relations to relate fluid properties on each side of a shock • describe and calculate the onset of simple instabilities Synopsis Introduction of Lagrangian and Eulerian derivatives. Derivation of the vector form of the equations of conservation of mass, momentum and energy. Brief review of simple equations of state. Introduction of the concept of vorticity and the essentials of vorticity dynamics. Bernoulli's equation with simple examples. De Laval nozzle flow and transition to supersonic flow.

Basic introduction to viscosity and its importance in boundary layers. Reynolds number. Stagnation point flows. Sound waves and formation of shocks. Conservation relations. Simple treatment of instabilities (convection, Rayleigh-Taylor, Kelvin-Helmholtz). Prerequisities There are no prerequisites. Recommended Books The Physics of Fluids and Plasmas by A R Choudhuri, Cambridge, ISBN:0-521-55543-4 Fluid Dynamics by G.K. Batchelor, Cambridge, ISBN:0-521-09817-3 Incompressible Flow by R.L. Panton, Wiley, ISBN:0-471-85505-7 Tutorials There will be four problem sheets, and four tutorials will be held to discuss these and other more general issues. Assessment 2-hour examination=100% There is no continuous assessment in this module.

PH4032 Special Relativity and Fields Semester 1 Available: each year Credits: 15 Number of lectures: 27 Lecturer: Dr N V Korolkova Overview Relativity is closely related to the concept of fields. Historically, Special Relativity emerged from the theory of electromagnetic fields. On a more fundamental level, the principle that every cause takes a finite time to have an effect on a different location calls for a mediator of interactions, a field. Every point in space may carry field strengths that could be scalars, four-

dimensional vectors, tensors, spinors etc. According to the principle of relativity, the field equations are the same in all coordinate frames that are in uniform motion relative to each other. Additionally, fields satisfy the Principle of Least Action and possible some internal symmetries. From these fundamental ideas follows a most remarkable wealth of connections in the physical world – Maxwell’s electromagnetism, the Lorentz force, the relativistic wave equations, antiparticles, spin etc. The theory of fields unifies classical physics and shows some general recipes for guessing the laws of Nature. Aims and Objectives To present a comprehensive theory of special relativity and an introduction to the theory of fields, including • derivation and the basic properties of the Lorentz transformations • space-time metric and proper time • tensors and spinors • relativistic dynamics, energy, momentum and forces • derivation of the Lorentz force from first principles • motion of charges in uniform electromagnetic fields • ideas of gauge invariance • electromagnetic potentials and the electromagnetic field tensor • derivation of Maxwell’s equations from first principles • Principle of Least Action for fields • Relation between symmetries and conservation laws • retarded potentials and electromagnetic radiation • energy-momentum tensor • derivation of the Dirac equation from first principles • transformations of Dirac spinors • antiparticles • local phase invariance and gauge fields • derivation of the Pauli equation including the gyromagnetic ratio of spins • charged waves in electromagnetic fields Learning outcomes By the end of the module, students will have a comprehensive knowledge of the topics covered in the lectures and will have acquired some important skills in theoretical physics, in particular to • derive relativistic dynamical laws and solve some of the resulting equations of motion • work with four-vectors, spinors and tensors, including their transformations • derive relativistic field equations such as Maxwell’s equations and the Dirac equation • calculate energy-momentum tensors • calculate retarded potentials • derive the non-relativistic limit • calculate wavc functions in magnetic fields

Synopsis 1. The principle of relativity (relativistic kinematics) 2. Relativistic mechanics (Lagrangian, energy, momentum, force) 3. Charges in electromagnetic fields (electromagnetic potentials, Lorentz force, field-strength tensor) 4. The electromagnetic field equations (dual tensor, Principle of Least Action, electromagnetic Lagrangian, four-dimensional current, Maxwell’s equations, retarded potentials, dipole radiation, energy-momentum tensor) 5. Relativistic matter waves (Dirac equation, transformation of Dirac spinors, antiparticles, non-relativistic limit and Pauli equation, Landau levels) Recommended book L D Landau and E M Lifshitz, The Classical Theory of Fields (Butterworth, Oxford, 2002) Tutorials There will be problem sheets every week covering the course and a few additional examples where the students can apply the acquired skills. The homework problems are marked. At least three class tutorials will be held to discuss the homework. Assessment 2-hour examination = 75% Continuous assessment = 25%

PH4034 Laser Physics 1 Semester: 1 Available: each year Credits: 15 Number of lectures: 27 Lecturer: Prof Wilson Sibbett Overview Although the first laser was demonstrated in 1960, a significant proportion of the underlying physics predates this in areas such as atomic physics, quantum physics, optics and spectroscopy. However the advent of lasers has opened up many exciting aspects of physics and the particular beam characteristics of lasers, notably the coherence and intensity, have proved to be of immense scientific and technological importance. By studying the basic physics of laser media together with the system configurations that facilitate a range of desirable options for their operation, it is possible to understand why lasers are in a special category of optical sources. By considering the gain media together with options for the various configurations of the lasers, we can have insights into system designs that in some

cases provide excellent spectral purity while in other instances broader bandwidth but ultrashort-pulse outputs (digital optics) can be produced. Although the subject of laser physics is more than forty years old, there is still much active development of lasers, associated optical amplifiers and related devices, and their applications in everyday life from sophisticated high capacity communications to simple supermarket scanners continue to grow. Learning outcomes Within the course structure offered, students will gain a good understanding of the building blocks of lasers. In particular, they will be able to appreciate how the choice and fundamental characteristics of some laser materials and the optical cavities that are used serve to determine the ultimate behaviour of a laser system. This will involve aspects of atomic and molecular physics, beam optics and relevant laser physics for media that may be in solid state or liquid or gas phases. The design of lasers for particular output beam specifications and some of their most likely applications will also be presented. Students should therefore have a significantly enhanced understanding of how lasers work and which types of lasers are most relevant for specific performance specifications and subsequent applications. Synopsis

This course represents a relatively broad coverage of subject matter relating to the operating principles of lasers through to the physics that underlies specific choices of configurations and associated key characteristics. At the outset, the requirements that arise for the establishment of a population inversion are considered followed by relevant gain-threshold and gain-saturation dynamics with reference to homogeneous and inhomogeneous spectral broadening in the laser media. Examples are included for a range of distinctive laser types in which particular characteristics of solid-state, liquid and gaseous media are exploited. The subsequent structure of the course is then built on this foundation such that the spatial, spectral and temporal control of the outputs from lasers can be described in turn. This involves physical descriptions being presented on the topics of resonator stability and transverse modes, longitudinal resonator modes with spectral narrowing and tuning, and for the temporal domain techniques that include Q-switching, cavity dumping and mode locking. Relevant implementations of the lasers are mentioned briefly throughout this course to illustrate the suitability of these coherent light sources to a range of applications. Recommended books Siegman, Lasers, University Science Books Yariv, Introduction to Optical Electronics, Holt, Rinehart & Winston Svelto, Principles of Lasers, Plenum (All are suitable reference texts – copies in the library) Assessment

2-hour examination = 100%

PH4035 Principles of Optics Semester: 2 Available: each year Credits: 15 Number of lectures: 27 Lecturer: Dr. F. Koenig Aims and Objectives Modern experimental physics relies on optical techniques in a variety of research fields going far beyond the optical sciences. This course builds on the knowledge of optics acquired in first and second year to make students familiar with the underlying physical principles of optical devices used in experiments today. Learning Outcomes By the end of the module, the students will have a comprehensive knowledge of the topics covered in the lectures and will be able to: • understand more complicated subjects in the field of optics related to a future research

project. • describe the polarization properties of light with different theoretical concepts and

understand most polarization phenomena • understand the physics at interfaces of different refractive index; in particular for

designing multilayer systems. • calculate the resolving power of a device in order to resolve a spectral feature in an

optical signal. • measure coherence properties of light and use them for measurements. • solve diffraction problems in various geometries and obtain corresponding diffraction

patterns. • design optics for Gaussian beams and resonators by using the complex q-parameter. • know the concept of second harmonic generation. Synopsis Review of Maxwell’s equations, linear wave equation, plane waves, Poynting-vector. Physical origin of refractive index, dispersion model, Sellmeier equation. Polarisation: linear, circular, elliptical polarisation, Jones vectors and Jones matrices. Production of polarised light by various techniques, wave plates. Light at interfaces: Boundary conditions, Snell’s law, Fresnel equations, Energy conservation at interfaces, Brewster’s angle, total internal reflection, phase changes.

Multilayer films: Simple approach, vector calculus. Fabry-Perot interferometer. Finesse, resolving power, Michelson interferometer Coherence: spatial vs. temporal coherence, correlation coefficient, Wiener Khintchine Theorem, Van Zittert-Zernicke Theorem, Hanbury –Brown Twiss experiment. Diffraction: Huygens principle, Kirchhoff theory, Fraunhofer and Fresnel reflection, Babinet’s principle, calculation of diffraction patterns. Gaussian beams: Solution to wave equation, higher order and fundamental modes, q-parameter, spot size and radius of curvature, ABCD matrices, focussing, collimating and resonators. Nonlinear optics: nonlinear polarisation, second-harmonic generation, phase matching. Prerequisites There are no prerequisites other than a knowledge of elementary optics and basic mathematics. Recommended Books: The principal book is An introduction to modern optics by Grant R. Fowles Paperback: 336 pages, Dover Pubns; 2nd edition (1989) ISBN: 0486659577. A less compendious and standard book is Optics (4th Edition) by Eugene Hecht, Hardcover: 680 pages Pearson Addison Wesley; (2001) ISBN: 0805385665. A book easier to understand is Introduction to Optics by Frank L. Pedrotti and Leno S. Pedrotti, Paperback, Pearson Higher Education; (1992) ISBN: 0130169730. Tutorials Whole class tutorials will be held about every two weeks, where solutions to problem sheets and general question about the lecture material will be discussed. Assesment Continuous assessment: 25%; 2-hour examination = 75%. Continuous assessment via written solutions to problems.

PH4036 Physics of Music Semester: 1 Available: each year

Credits: 15 Number of lectures: 27 Lecturer: Dr Jonathan Kemp Overview Musical instruments function according to the laws of physics contained in the wave equation. Wind instruments, the human voice and the acoustics of concert halls can be explained largely by considering waves in the air, but understanding drums, percussion, string instruments and even the ear itself involves studying the coupling of waves in various media. The concepts of pitch, loudness and tone are all readily explained in quantitative terms as are the techniques that musicians and instrument makers use to control them. The analysis of musical instruments naturally culminates in a look at how musical sound may be synthesized. Learning Outcomes Students will have acquired an understanding of the physical principles involved in the listening, analysing and synthesizing of musical sounds. They will be able to appreciate the physics of acoustic resonators and excitation mechanisms and how these are utilized in various musical instruments. Synopsis Beats, series, complex Fourier transform. Plucked, struck and bowed strings. Air damping. Transverse vibrations of bars. Vibrating membranes and plates. Coupled Oscillators. Wave equation in air. Transmission and reflection, losses and radiation. Standing waves, pipes, cavities and waveguides, cross-section changes, resonators. The ear and perception of pitch and timbre. Scales and temperament. Stereo sound and brain processes. Reverberation and architectural acoustics. Transducers (loudspeakers, microphones and pickups). Case studies on strings, drums, woodwind, brass, and voice. Synthesizing musical sound (additive, subtractive, FM, wave-table and physical modeling). Prerequisites Admission to the honours class in physics and astronomy Prior or concurrent attendance at PH3066 Mathematics for Physicists Recommended Books Lawrence Kinsler, Austin Frey, Alan Coppens and James Sanders, Fundamentals of Acoustics (Wiley) Neville Fletcher and Thomas Rossing, The Physics of Musical Instruments (Springer) Juan Roederer, The Physics and Psychophysics of Music (Springer-Verlag) Tutorials

There will be at least three whole class tutorials to discuss general issues, timed according to demand of the class. These are often requested to be held close to the examination. Problem sheets will be issued, the answers to which will be discussed in whole group tutorials. Assessment 2-hour examination = 100%

PH4105 Physics laboratory 2 Semester: 1 Available: each year. Credits: 15 No. of Sessions: 20 afternoon sessions of three and a half hours each. Module Co-ordinator: Professor Malcolm H. Dunn Overview This experimental physics module builds on the Physics Laboratory 1 module, although it may also be taken as a stand-alone module with appropriate choice of the topics covered. This module is also made up of a set of sub-modules, each one lasting for five afternoon sessions with students undertaking four sub-modules in the course of the semester. Sub-modules presently on offer include Optics and Spectroscopy, Semiconductors/X-rays, Signal Processsing, Phase Transitions in Nickel Powders, and LabView. These may change, for example as new experiments are introduced. Descriptions of the present sub-modules are given below. The class is divided into self-selected groups, usually of eight persons, which then circulate around the sub-modules sequentially. The structure of the sub-modules differs from one to another. In some, students work on the same set of experiments, usually in pairs. In others, there are a number of experiments based on a common theme; following an introductory overview, students work singly or in pairs on specific experiments. Some of the sub-modules conclude with feedback sessions where students present the outcomes of their experimental work to their peers and demonstrators, followed by discussion. Other sub-modules aim at building basic skills such as in signal processing or computer-based data handling. All the experiments are up-to-date and relevant to the training of a practising physicist, with a number of the experiments closely related to those found in contemporary research laboratories. The variety of approaches offered ensures that you will find this laboratory both enjoyable and stimulating. The first session is taken by the class as a whole and includes an important safety seminar, covering electrical, chemical, cryogenic and laser safety, followed by practical advice on the keeping of laboratory note-books, etc. Aims & Objectives

To give you practical experience of some pervasive experimental techniques relevant to a practising physicist, e.g. signal processing, computer-based data handling, optical spectroscopy, x-ray crystallography. To introduce you to important contemporary developments in experimental physics, e.g. squids, lasers, Fourier transform spectroscopy, holography. To strengthen your understanding of important physical concepts, e.g. phase transitions, semiconductor physics, superconductivity. To develop sound practice in a number of important generic skills such as planning of experiments, risk assessment, record keeping, data handling and evaluation, error analysis, drawing evidence-based conclusions, identifying future work. To enhance manual and mental dexterity at performing experiments. To develop transferable skills with regard to the presentation of research outcomes through both written work and oral presentations. To gain experience of carrying out experimental work while working alone, in partnership, and in small groups. Learning Outcomes You will have acquired: familiarity with a range of important and pervasive experimental techniques, practical experience of contemporary experimental equipment, including some used in present-day research laboratories, a fuller understanding of a range of important physical concepts through exploring them in experimental situations, key generic skills required by an experimentalist in the physical sciences, encompassing documentation, assessment, deduction, and presentation, ability to work both on your own and collaboratively. Synopsis Phase Transitions in Nickel Powders (PT) The experiment is to investigate the dynamics and cooperative effects of a fine ferromagnetic powder when agitated by electric and/or magnetic fields. A team of four will be expected to divide up the tasks needed to understand the electrostatic and magnetic forces involved in moving the grains; investigate the appropriateness of the design of the cell containing the powder and the coils for producing the magnetic field and of interfacing a video camera and instrumentation using LabView. The cooperative effects between the grains depend on the level of excitation in a way that loosely corresponds to phase transitions as a function of temperature. Success would be a 'phase diagram' for the system. LabView (LV) LabVIEW is an industry-standard programming and control environment. It is used throughout science and engineering as a means of creating programs, and is ubiquitous in laboratories that require instrument control. A familiarity with LabVIEW is therefore a very saleable transferable skill. The purpose of this sub-module is to give the student an introduction to programming and the use of LabVIEW. By the end of this sub-module the student should be able to build a LabVIEW virtual instrument (VI) to undertake a specified task. The sub-module develops the student through finding out about the LabVIEW

environment, ensuring they become familiar with the various windows, menus and tools. Next a simple VI is created, edited and debugged. The use of sub-VIs is discussed and two means of creating these undertaken; including setting up an icon and connector pane. Loops, program structures, arrays, charts and graphs are also introduced and used in the development of various VIs. The lab culminates in using LabVIEW’s control ability to interrogate a GPIB instrument simulator. The student learns how to communicate with a GPIB instrument, and puts into practice some of the newly developed skills in interpreting and visualising simulated experimental measurements. At the end of these four afternoons the student will have the skill needed to start using LabVIEW to tackle future projects. Optics and Spectroscopy This aims to give practical experience of important techniques in modern optics, particularly in spectroscopy. The first three afternoons are spent on work in pairs and small groups involving spectroscopy with prisms, gratings, Fabry-Perot interferometers, and a Fourier transform spectrometer. One experiment measures the splitting of spectral lines in neon in a magnetic field. A tunable coherent optical source is demonstrated. The final two afternoons are spent on an experiment of the student's choice in the area of optics and spectroscopy. These final two afternoons aim to develop experimental planning and design skills as well as the investigation techniques and exploring of science that are practised in the first three afternoons. Semiconductors/X-rays/SQUIDS Semiconductor Band Gap. In this experiment the temperature dependence of the resistivity of germanium is measured at high and low temperatures to obtain the band gap of intrinsic germanium and the impurity activation energy. These are combined to determine the exhaustion range and the temperature dependence of the mobility. The next task is to estimate the density of the gold doping in the samples, and the final part of the experiment is to investigate the importance of four terminal measurements for a metal semiconductor junction. Superconducting Quantum Interference Devices- SQUIDS. This experiment serves as an introduction to superconductors and in particular to high temperature SQUIDS. These allow us to measure very small levels of magnetic flux and a variety of related quantities such as voltage. The actual measurements are very simple, but the background theory and understanding are not! The Structure of Solids via X-ray Diffraction X-ray diffraction is one of the most important analytical tools for characterising crystalline solids. The aim of the experiment is to introduce the technique and to lay the basis for an understanding of the interaction of waves of all types with regular lattices. The experiment itself is relatively simple, however the interpretation of the data has several subtleties and will require more thought. You will also be required to discuss the significance of the experiment and possible developments to improve the apparatus. Specific goals include measurement of the inter-atomic and inter-planar spacing in a sodium chloride crystal. Signal processing The overall objective of the signal processing sub-module is to give an understanding of the basic principles of noise and of signal recovery. The module is roughly divided into two sections: the first (and larger) part is a practical introduction to the use of phase sensitive detection (PSD) methods, important ideas which are used in measurement systems over a

huge range of applications. The second part of the module provides a basic introduction to the use of digital storage instruments in measuring signals, and in recovering them from noise. Pre-requisites The only requirement is entry into the JH class. Recommended Books and Other Literature No book is recommended covering the whole of this module. For each sub-module students will receive handouts providing a general introduction, including references to review articles and other recommended reading material. Additional documentation provides more detailed information required for the experiment. Students are encouraged to carry out literature searches appropriate to the experimental work they are undertaking. Laboratory Notebook It is important that students keep up-to-date and properly laid out lab books. Advice on this will be given at the first session. Assessment Assessment for each sub-module involves marking of the experimental work (around 70%), along with a test or presentation (around 30%). Assessment procedures differ from topic to topic, and demonstrators will advise on particular arrangements for each topic. All topics are weighted equally in the calculation of the final mark and grade.

PH4111 Project in Physics 1 Semester: whole year Available each year Credits: 30 Overview The project aims to develop students’ skills in searching the physics literature, in experimental and observational design, the evaluation and interpretation of data, and the presentation of results. The main project is preceded by a review essay on a topic which may be related to the theme of the project or may be unrelated to it. There is no specific syllabus for this module. Students taking the BSc degree select a project from a list of those available and are supervised by a member of the academic staff. Students taking an MPhys degree are not normally permitted to do this module. Assessment

Project and oral examination = 100%

PH5002 Foundations of Quantum Mechanics Semester: 1 Available: each year Credits: 15 Number of Lectures: 27 Lecturer: Dr K K Wan Overview This introduces students to the modern Hilbert space formulation of quantum mechanics and to relativistic quantum mechanics. Aims and Objectives The emphasis is on developing a good understanding of the mathematical and conceptual foundations of the subject. To achieve this the module is presented in several parts: Part 1 introduces Hilbert spaces, operators and the spectral theorem. Part 2 sets out the basic postulates of quantum mechanics. Part 3 discusses operator theory of angular momentum, including orbital and spin angular momentum and their addition. Part 4 consists of an introduction of relativistic quantum mechanics Learning Outcomes Having taken the module students should have gained a good knowledge of the mathematical techniques employed in modern physics and a good understanding of quantum mechanics in an axiomatic manner. In particular students should have a good knowledge of • operator theory in Hilbert space, particularly selfadjoint and unitary operators, projectors and the spectral theorem for selfadjoint operators and properties of commuting selfadjoint operators, • the basic postulates on quantum statics and dynamics, including the working of various Pictures to describe quantum evolution, • the use of creation and annihilation operators, • quantum entanglement, • operator theory of angular momentum and their addition, • Charged spin-half particle in external magnetic field, • Klein-Gordan and the Dirac equations and the relativistic origin of spin. Synopsis The module is presented in several parts:

Part 1 introduces Hilbert spaces, starting from finite-dimensional vector spaces, and operators in Hilbert space, , including selfadjoint operators, unitary operators, projectors, and the spectral theorem. Part 2 sets out the basic postulates of quantum mechanics, illustrated by many examples and applications, including of quantum measurement problems, use of creation and annihilation operators, quantum evolution in terms Schrodinger, Heisenberg and Interaction pictures, quantum statistical ensembles and quantum entanglement. Part 3 discusses operator theory of angular momentum, including orbital and spin angular momentum and their addition and application to the Zeeman effect Part 4 consists of an introduction of relativistic quantum mechanics, including the Klein-Gordan and the Dirac Equations and the relativistic origin of spin. Prerequisites PH3061 and PH3062 Recommended Books C J Isham, Quantum Mechanics (Imperial College Press) A Z Capri, Nonrelativistic Quantum Mechanics (Benjamin/Cummings) R W Byron and R W Fuller, Mathematics of Classical and Quantum Physics, Vol 1 (Addison Wesley) Tutorials There are five tutorial sheets and some whole class tutorials to discuss important issues. Assessment 2-hour examination=100%.

PH5003 Group Theory Semester: 1 Available: each year Credits: 15 Number of lectures: 27 Lecturer: Prof J F Cornwell Overview Most physical systems possess some symmetry. In some cases these are geometrically obvious. For example atoms have spherical symmetry and crystals have both translational and rotational symmetry. However, in other situations, such as in the theory of fundamental

particles (quarks, gluons, etc), symmetry concepts are still very vital even though they may not be intuitively obvious geometrically. Group Theory provides a systematic way of dealing with all the types of symmetry that appear in physics, and extracting the maximum amount of information that results from the symmetry. Aims and objectives To present all the necessary ideas on group theory and show how they can be applied to the quantum mechanical study of physical problems that possess symmetry. Learning Outcomes By the end of the module, the students should have a good knowledge of the topics covered in the lectures, and should: • be able to appreciate the predictive power that group theory provides, • be able to interpret and use the published tables of characters that appear in the literature, and • be conversant with abstract algebraic concepts and their application to physics. Synopsis An introductory survey, involving: the definition of a group, with physically important examples, a detailed treatment of rotations and translations, the connection with quantum mechanics, the basic concepts of `abstract' group theory (subgroups, classes, cosets, factor groups, homomorphic and isomorphic mappings, direct product groups, etc), for which no previous knowledge is assumed, basic ideas of the theory of Lie groups, starting with a definition, and including the concepts of connectedness, compactness, and invariant integration, theory of matrix representations of groups, including the ideas of equivalent representations, reducible and irreducible representations, unitary representations, characters, projection operators for determining basis functions, direct-product representations, irreducible tensor operators, and the Wigner-Eckart theorem, applications to quantum mechanics, including solving the Schrodinger equation, determining selection rules and transition probabilities.

Prerequisities Some previous knowledge of quantum mechanics, including perturbation theory. Some knowledge of matrices. No previous knowledge of group theory is assumed. Recommended books Group Theory in Physics - An Introduction by J F Cornwell (Academic Press 1997) or Group Theory in Physics - Volume I by J F Cornwell (Academic Press 1984, being reprinted June 2004). Tutorials Problems sheets will be handed out, and the solutions of these and other related matters will be discussed in whole class tutorials which will be held at various stages of the course. The total time allocated to whole class tutorials will be about three hours Assessment 2-hour examination = 100% There is no continuous assessment in this module.

PH5004 Quantum Field Theory Semester: 1 Available: each year Credits: 15 Number of lectures: 27 Lecturer: Dr A G Green Overview Quantum field theory combines classical field theory with quantum mechanics and provides analytical tools to understand many-particle and relativistic quantum systems. This course aims to introduce the ideas and techniques of quantum field theory. I will use examples drawn mainly from condensed matter physics to illustrate the ideas and application of quantum field theory. Aims and Objectives To present an introductory account of the ideas of quantum field theory and of simple applications thereof, including

• Quantization of classical field theories. • Second quantization of Bosons • Failure of single particle interpretation of relativistic quantum mechanics • Second quantization of fermions • Solving simple models using second quantization • Feynman’s path integral approach to quantum mechanics and its relation to classical action principles. • Field integrals for bosons and fermions. • Relationship between path integral methods and second quantization. • Descriptive introduction to Green’s functions and Feynman diagrams in quantum field theory. Learning Outcomes By the end of the module, students will have a comprehensive knowledge of the topics covered in the lectures and of their application in solving simple problems. They will • Understand the canonical quantization of classical field theories. • Understand and motivate the second quantization of relativistic quantum theories. • Diagonalize simple quantum field theories using unitary transformations, Bogoliubov transformations and Fourier transforms. • Identify the mode energies in such theories. • Understand the conceptual basis of Feynman path integrals. • Calculate simple path integrals. • Understand field integrals and their relation to second quantization. • Give a descriptive exposition of the use of Green’s functions and Feynman diagrams in quantum field theory. Synopsis Coupled quantum harmonic oscillators, canonical quantization of classical field theory, bosonic quantum field theory. Second quantization for bosons. Relativistic quantum mechanics. The Klein-Gordon and Dirac equations. Failure of single particle interpretation. Second quantization of quantum fields. Second quantization for Fermions. Diagonalizing simple quantum field theories by unitary rotations, Bogoliubov transformation and Fourier transformations. Identifying normal modes. Models of interacting spins. The Heisenberg model. Representing spins in terms of bosons: Holstein-Primakov and Schwinger bosons. Examples: weakly interacting bosons and bose condensation, phonons in a bi-partite lattice, Heisenberg ferromagnet, Friedel oscillations and BCS theory. The Feynman Path integral treatment of quantum mechanics. Relation to classical principle of least action. Relationship to statistical mechanics.

Bosonic Coherent States. Bosonic Field Integrals. Grassman variables, fermionic coherent states and fermionic field integrals. Solving simple problems using functional integration. Example weakly interacting Bosons. Brief descriptive introduction to Feynman Diagrams and Green’s functions in quantum field theory and many-body physics. Prerequisites PH4028, PH4029 Corequisite PH5002 Recommended Books As yet, there is no one book which covers all of the material in the course in one place. However, Profs. A. Altland and B. D. Simons will publish a book with CUP (due out in January 2005) which does. Although this book will not be published in time to be directly useful for the course, Prof Simons has a web page with lecture notes, problem sets and solutions at http://www.tcm.phy.cam.ac.uk/~bds10/tp3.html I will make liberal use of these notes (with kind permission of Prof Simons) and will provide a hard copy in the library. These notes cover more material than I will cover in the course. I will also provide copies of lecture notes of Prof. A. Schofield (with kind permission of Prof Schofield). These notes provide a less formal treatment of the material, at a more appropriate level for the course. The section on functional integrals will be extended in my presentation. I will provide notes for any parts not covered by either of these two sets of notes. Other books which may prove useful: Second Quantization: C. Kittel Quantum Theory of Solids Wiley (1963) Not to be confused with the Introduction to Solid State Physics by the same author. Very good introduction to second quantization R. P. Feynman Statistical Mechanics, Benjamin, New York (1972). A classic text. Very good introductions to second quantization and many-body physics. Path Integrals and Functional Integrals R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, New York (1965) Classic introduction to the Feynman path integral. Many modern advances not included, but a great read nevertheless J. W. Negele and H. Orland, Quantum Many-Particle Systems, Addison-Wesley Publishing (1988) Covers both second quantization and path integrals in some detail. A.Das, Field Theory: A Path Integral Approach, World Scientific Publishing (1993) A good introduction to the path integral approach (cheap too!) Relativistic QM J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics, McGraw-Hill (1964) L. H. Ryder Quantum Field Theory, CUP (1996)

Tutorials Problem sheets and tutorials will form an essential and integral part of the course. There will be 7 problem sets and at least the same number of whole class tutorials to discuss these and other issues. A sample examination will be given and answers will be expected to be handed in for marking and return Assessment 2-hour examination = 100% There is no continuous assessment in this module.

PH5005 Laser Physics 2 Semester: 1 Available: each year Credits: 15 Number of lectures: 27 + 4 whole class tutorials. Lecturer: Professor Malcolm H. Dunn. Overview The course is designed to introduce the student to the classical and semiclassical treatments of laser physics. In the former both the electromagnetic radiation and the active medium of the laser are treated classically, while in the latter although the radiation is still treated classically, the active medium is now treated quantum mechanically. These two broad approaches are treated with varying levels of sophistication. For example the radiation may be treated by Maxwell’s equations while the active medium may be described through the time-dependent Schrodinger equation. Alternatively a simple rate equation model may be adopted. In this course a number of these variations are explored with regard to their applicability and limitations. The course is delivered through a “Powerpoint” presentation, accompanied by paper handouts of most of the slides, and with PDF versions available for downloading through the University web. Learning is assisted through the incorporation into the course of animations and numerical modelling material. (The latter is the “Psst” software, which may be downloaded free for personal use.) The course will in part involve the further development of topics introduced in Laser Physics 1 to a level allowing quantitative problem solving. Aims and Objectives

The course aims to develop a working knowledge and conceptual understanding of important topics in contemporary laser physics at a quantitative level. A key objective is to enable the student to undertake quantitative problem-solving relating to the design, performance and applications of lasers through thereby acquiring an ability to put such knowledge into practice by way of numerical calculations. The aim throughout is to provide a thorough grounding in basic principles and their application, so that by the end of the course the student will have acquired a range of essential skills and knowledge required by a practitioner of laser physics and engineering. Such knowledge of the basics will be of enduring value and relevance. It will enable the student to innovate, design and analyse laser devices and systems at a quantitative level. As well as developing the conceptual framework the course also aims to give a sound perspective of contemporary trends and developments in laser physics, particularly with regard to new schemes for the generation of coherent electromagnetic radiation and the associated devices. Learning Outcomes You will have acquired: • A conceptual understanding of the classical and semi-classical approaches to laser physics, and a perspective of their areas of applicability. • An ability through a thorough grounding in the rate equation and strong signal approaches to analyse quantitatively the steady-state and dynamical performance of important contemporary laser devices. • A comprehensive knowledge, including of recent developments, concerning: solid- state lasers (including diode-laser pumped devices), semiconductor lasers, fibre lasers, vibronic and other tuneable lasers, organic lasers, laser amplifiers, and newly emerging gain media. • An ability to both analyse quantitatively and to design such lasers. • A conceptual understanding of such important aspects of laser active media as linewidth determining processes, dispersive/gain properties, spatial and frequency hole-burning, and coherent/random processes (Rabi flopping). • An ability to both describe quantitatively and analyse such effects. • A thorough grounding in the principles and design of laser resonators including both stable and unstable cavities. • An ability to analyse quantitatively and design such cavities by using matrix techniques, geometrical modelling techniques, or virtual source techniques. • Access to and familiarity with numerical modelling tools (including “Psst”) relating to many aspects of laser design and performance. Synopsis Rate Equation Approach to Laser –Steady-State behaviour –Transient effects –Relaxation Oscillations

–Q-switching –Cavity Dumping Modelling of Solid-State Lasers –Diode-laser-pumped solid-state lasers Optical Amplifier –Linear Gain Regime –Power Extraction –Pulsed amplifiers Dispersion & Gain in Laser –Electron Oscillator Model –Dispersion Relations –Mode Effects Review of Stable Optical Resonators –Matrix Techniques –Geometrical Optics Techniques Unstable Resonators –Applications –Virtual Source Technique Coherent Processes –Rabi Oscillations –Macroscopic Polarisation –Semiclassical Approach to Laser Linewidth of Laser Oscillator –Schawlow-Townes Limit –Other Influences Fibre Lasers Vibronic Lasers –Tuning Techniques –Linewidth Control –Frequency Stabilisation Organic Lasers Semiconductor Lasers –VCSL’s –Optical Pumping –Quantum Cascade Lasers –Quantum Dot Lasers Novel & Emergent Gain Media Pre-requisites PH3061, PH3062, (PH3064 and PH3065) or PH3007, PH4034. Recommended Books For Purchase: •Principles of Lasers, O. Svelto, Plenum, 1998, 4th Ed. For Consultation:

•Optical Electronics in Modern Communications, A. Yariv, Oxford University Press, 1997, 5th Ed. •Optical Electronics, A. Yariv, Holt-Saunders, 1991, 4th Ed. •Quantum Electronics, A. Yariv, Wiley, 1989, 3rd Ed. •Optoelectronics: An Introduction, J. Wilson & J. F. B. Hawkes, Prentice Hall, 3rd Ed. •Lasers, A. E. Siegman, Oxford University Press, 1990 (ISBN 0-19-855713-2). •Lasers, Invention to Applications, Ed. J.H. Ausubel & H.D. Langford, National Academy Press (Washington, DC), 1987. Other Sources •Library (Arthur Maitland Collection) •Popular Journals (e.g. Laser Focus) •Websites. (Optics Express) •Journals: –Optics Letters –Applied Physics Letters –IEEE J. Quantum Electronics –J. of Optical Society of America –Applied Physics B –J. Modern Optics – Science, Nature. –Optics & Photonics News {Many of these journals are now available for consultation electronically). Tutorials Four whole class tutorials distributed throughout the course. Assessment 2-hour examination = 100%.

PH5008 Optoelectronics and Nonlinear Optics 2 Semester: 2 Available: Alternate years 2007-2008, 2009-10 etc. Number of lectures: 27 Credits: 15 Lecturer: Prof T F Krauss Overview Optoelectronics is generally understood as the union of electronics and optics. Optoelectronics is mainly concerned with the generation, manipulation and detection of light in electronic materials. These materials are typically semiconductors, e.g. silicon and gallium

arsenide, but can also be more exotic such as liquid crystals and organic semiconductors. Optoelectronics is all-pervasive and covers a large number of everyday applications, ranging from the ubiquitous LED, televisions and computer displays, as well as lasers in CD players, to sophisticated equipment for high-speed telecommunications applications that form the backbone of the internet. One of the key drivers of the field is the utilisation of optoelectronic devices in telecommunications systems. This has led to a true revolution in our lives, enabling wireless and internet services and soon leading on to video-on-demand. As communications systems continue to increase capacity, photonics and optoelectronics are the key enabling technologies, leading to the availability of ever faster systems, and eventually all-optical signal processing. Aims and Objectives Building on previous coursework, the module will deepen the understanding of photonic and optoelectronic devices. The electromagnetic theory of the propagation of light in optical fibres and waveguides enables a better description of the phenomena utilised in practical devices. This will lead to a better appreciation of the many exciting physical concepts utilised in optical telecommunications systems and networks, as well as their limitations. Learning Outcomes Students will gain an appreciation for the wide range of optoelectronic principles and devices used in everyday life and how the physical principles studied in previous modules are exploited in such devices. They will deepen their understand of the principles of confining light in optical waveguides and fibres and how these principles are used in optical telecommunications systems and networks. The module will feature a considerable element of interactivity where the students will develop their research skills as well as their ability independently to acquire and evaluate information, e.g. in small group projects, literature searches and presentations. Synopsis In PH4027 (ONLO I), optical waveguiding was introduced using geometrical optics. Here, we will derive the full waveguide description from Maxwells equations, thus using the proper electromagnetic description. The electromagnetic model allows the full description of modes in optical waveguides and fibres, as well as their interaction. This leads to coupled mode theory, e.g. in directional couplers and Bragg gratings, and passive photonic devices in general.

Then follows the description of photonic integrated circuits that combine active and passive waveguide elements, such as integrated lasers and modulators, optical switches and cross-connects, wavelength converters and multiplexers. The prospects for all-optical signal processing will be discussed. Contemporary topics such Raman amplification in fibres and planar silicon as well as photonic crystals will be introduced. Prerequisites PH 3007 (previously PH3065) Electromagnetism PH 4027 Optoelectronics and Nonlinear Optics 1 Recommended books A. Yariv, "Optical Electronics in Modern Communications", Oxford University Press Assessment The module will be assessed both continuously and in a 2 hour exam. Continuous assessment consists of an essay and a presentation, accounting for 25% of the mark. The exam accounts for the remaining 75%.

PH5011 General Relativity Semester: 2 Available: each year Credits: 15 Number of lectures: 27 Lecturer: Dr H-S Zhao Overview General relativity is the name given to Einstein's theory of gravity. As the title suggests, it is more general than the special theory of relativity which he formulated some years earlier. But the difference between the two does not merely reside in the fact that the special theory is restricted to a description of physics based on inertial frames of reference whereas the general theory can deal with physics referred to accelerated frames. Of greater significance is that the latter is a field theory in which the "field" is spacetime itself; the field equations determine how the curvature of spacetime is linked to the distribution of matter, and the geodesic equation (the "equation of motion") tells us how matter moves at any point in the field. These theoretical postulates allow us to solve astronomical problems including planetary motion and the bending of light, and give insights to cosmology and the properties of black holes.

Aims and Objectives To present an introductory account of the theory of general relativity and of experimental tests of the theory, including • tensor theory - the mathematical basis of the subject, • the reasons why Newton's theory of gravity is inadequate, • the three principal postulates of the theory, and the reasons why Einstein was led to their formulation, • the solution of the field equations for a static, spherically-symmetric source, • the three classic experimental tests of the theory, and more recent and current experiments, • the application of the theory to black holes. Learning Outcomes By the end of the module, students will have a comprehensive knowledge of the topics covered in the lectures and will be able to • distinguish between contravariant and covariant tensors, • state the importance of the metric tensor, the significance of covariant differentiation and the distinction between flat and curved spaces, • calculate the components of the curvature tensor for simple two dimensional examples, • demonstrate that the postulates of general relativity are consistent with Newtonian gravitational theory in the weak field, quasi-static limit, • calculate Christoffel symbols for a static, spherically symmetric gravitational source, • solve some of the simpler problems involving particles and photons moving in the neighbourhood of such a source, • calculate infinitesimal length elements and time intervals for any spacetime in which there are three spatial coordinates and one time coordinate. Synopsis Review of inertial frames, special relativity and Newtonian gravity. The principle of equivalence.

Basic techniques of tensor analysis. Contravariant and covariant tensors. Tensor contraction. Riemannian spaces, the metric tensor and its conjugate, raising and lowering of suffices. The geodesic equation in variational and differential form; Christoffel symbols. Riemannian coordinates, covariant derivatives. Flat and curved spaces. The curvature tensor, Ricci tensor, and Einstein tensor. How matter is described on a large scale. The stress-energy tensor for a perfect fluid. The field equations of general relativity. Distances, time intervals, speeds. Reduction of equations of general relativity to Newtonian gravitational equations in the weak field, quasi-static limit. Schwarzschild exterior solution, the physical significance of the coordinates. Embedding a curved space in a flat space of higher dimensions. The interior solution for a source of constant density. Observational tests of general relativity Planetary motion, bending of light rays, gravitational frequency shift. The Hafele-Keating experiment. Radar echoes from planets. Black holes, gravitational collapse. Prerequisites There are no prerequisites other than an elementary knowledge of special relativity - which students will have obtained in the Physics 2A module or elsewhere. Recommended books The principal book is General Relativity and Cosmology by T L Chow (Wuerz 1994) Much of the book is directly relevant to the course, and the remaining chapters offer a good introduction to cosmology. For the early sections on tensor theory, a useful text is Tensor Analysis by J L Synge and A Schild (Univ of Toronto Press 1949) There are now a number of additional modern books, probably inspired by the upsurge of astronomical relevance of the topic, among which are Gravity by J B Hartle (Addison Wesley 2003) and General Relativity by J L Martin (Prentice Hall 1995) Tutorials There will be three problem sheets, and at least three whole class tutorials will be held to discuss these and other more general issues. A sample examination question will be given out and answers will be expected to be handed in by a due date for marking and return. Assessment:

2-hour examination = 100% There is no continuous assessment in this module

PH5012 Quantum Optics Information not yet available

PH5013 Superconductivity Semester : 2 Available: Each year Credits: 15 Number of Lectures: 18 Lecturer: Dr A G Green and others Overview When many metals are cooled below a certain temperature they undergo a transition to a state where currents can flow without resistance. This state also has other curious properties, such as the ability to shield perfectly external magnetic fields from its interior. This behaviour can ultimately be traced to a collective behaviour of the conduction electrons, which become more ordered at low temperature, in the sense that their wavefunctions bear a common phase relation to one another. This state has some features in common with Bose condensates. These unusual properties originate at a microscopic level from the ability of electrons to interact with each other in solids in a way that would not be possible in free space. The phase coherence of the superconducting electrons leads to macroscopic quantum phenomena, such as the quantisation of magnetic flux in a superconducting circuit. While extremely interesting from a theoretical point of view, the potential applications of superconductivity are many, including: sensors of tiny magnetic fields (SQUIDS); lossless power transmission; frictionless bearings; magnetic levitation (including floating passenger trains); high magnetic fields; quantum computers. Aims and Objectives To produce an introductory account and elementary understanding of: • Electron – phonon coupling, Cooper pair formation and BCS theory • The use of free energy models to describe the phenomenology of the superconducting state • The electromagnetic behaviour of superconductors • The understanding and consequences of macroscopic phase coherence

• The magnetic phases of type I and type II superconductors Learning Outcomes By the end of the course, students will have a comprehensive knowledge of the course content and will feel confident to: • Tackle elementary problems in superconductivity using electromagnetism, Ginzburg- Landau theory and the concept of macroscopic wavefunctions. • Be able to read topical papers on superconductivity and be able to know where to begin to understand the essential content. Synopsis Brief overview of the bulk properties of superconductors. Introductions to BCS theory including: The attractive electron interaction in solids. The electron-phonon interaction and Cooper pairs. The N-bodied wavefunction. Spin pairing and the symmetry of the spatial wavefunction. Macroscopic phase coherence. Quantum circuits, quantum tunnelling and quantum interference effects. Electromagnetic properties of superconductors. The Meissner effect. Free energy of superconductors in magnetic fields. The Ginzburg-Landau (GL) theory. The application of GL theory to type I and type II superconductors, including a description of a the Meissner state, the mixed state and derivation of the London form factor. Exotic superconductors and novel superconducting states. Applications of superconductivity. Prerequisites PH3002, PH3061 and PH3062. Recommended Books A highly readable introductory text is: Introduction to Superconductivity By A. C. Rose-Innes ,E. H. Rhoderick ,Rose-innes Paperback / Pergamon Press / January 1978 / 0080216528

The main text book will be: Superconductivity of Metals & Cuprates By J. R. Waldram Institute of Physics Publishing (September 1996) ISBN 0852743378 Useful supplementary text books are: Introduction to Superconductivity By Michael Tinkham Paperback 432 pages (April 1996) Publisher: McGraw-Hill Education (ISE Editions) ISBN: 0071147829 Superfluidity and Superconductivity D R Tilley and J Tilley Graduate Student Series in Physics Institute of Physics Publishing (September 1996) ISBN 0750300337 Tutorials In addition to the 18 lectures, there will be a number of additional activities including problems classes, directed reading sessions and a short oral examination based on the material covered in lectures and other aspects of the module. Assessment 2 hour examination = 75% Continuously assessed problems and tasks = 25%

PH5014 The Interacting Electron Problem in Solids Semester: 2 Available: every second year; next in 2007-08 Credits: 15 Number of lectures: 18 plus reading assignments and project work Lecturer: Prof A.P. Mackenzie Overview Traditional solid-state physics is based on the sweeping assumption that the Coulomb interaction between the electrons can be ignored or treated in a mean-field manner. Arguably the most amazing aspect of this assumption is that it has had any success at all – how can one construct, for example, a theory of metals that effectively ignores the charge of the electron? The answer lies in the fact that it is applicable only to a relatively restricted class of materials in which the wavefunctions of the outermost conduction and valence electrons are a reasonable approximation to plane waves. Modern solid-state physics is concerned with the vast number of more interesting cases in which this approximation breaks down, and the

electrons are said to be ‘strongly interacting’. This course will discuss how this takes place, and give an introduction to the subtle and beautiful theoretical treatments that have been developed for the study of the strongly interacting electron problem. Aims and Objectives To present an introduction to the physics of strongly interacting electrons in solids, motivating an appreciation of its place as one of the most important problems in modern science. Topics covered will include: • tight-binding theory for electronic band structure and the increasing absurdity of its underlying assumptions. • introduction to Landau’s many-body Fermi liquid theory of interacting electron metals. • direct spectroscopic probes of Landau fermion quasiparticles. • the single-band Hubbard model and its reduction to the t-J model • case studies of some of the classic examples of correlated many-body states such as the Normal and Fractional Quantum Hall States. Learning outcomes By the end of this module, students will have received a thorough grounding in an important field of physics that also impacts on other fields of science. This will have been achieved partly through the formal lectures, and partly through guided self-study via reading assignments. In particular, they will • understand the links between atomic and solid-state physics • appreciate the interplay between electron-lattice coupling and electron-electron interaction • have familiarity with some of the most famous ‘base models’ for interacting electron physics • have developed their ability to distil information from the original research literature Synopsis Review of the two limits of energy band theory (perturbations around the free electron limit and the atomic limit. Nearest-neighbour tight-binding bands and Fermi surfaces in two dimensions The concept of correlation from an examination of the hydrogen molecule The essential competition between kinetic and potential energy as expressed in the Hubbard model Re-examination of the hydrogen molecule to explain the concept of magnetic exchange Reducing the full Hubbard model to the ‘t-J’ model

The Mott-Hubbard insulating transition and remarks on magnetism The quasiparticle concept and Landau’s Fermi liquid theory Case studies of modern ‘quantum ordered’ correlated electron states. Prerequisites For those following the St. Andrews undergraduate degree: Solid State Physics, Quantum Mechanics 1 and Quantum Mechanics 2. The course will also be suitable for graduate students, who should discuss their previous courses directly with Prof. Mackenzie. Recommended books There will be no dominant course book, but sources will include: Taylor & Heinonen, A Quantum Approach to Condensed Matter Physics; Ashcroft & Mermin, Solid State Physics; The Feynman Lectures on Physics, vol. 3; Abrikosov, Gorkov & Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Ch 1 only is at the level of this course); Ziman, Principles of the Theory of Solids; Singleton, Band Theory and Electronic Properties of Solids. Tutorials A number of formal tutorial problems will be set, with solutions explained during whole-class tutorials. In addition, some special reading assignments will be given, with the student tasked with explaining the topic to his/her peers during a short tutorial lecture. Assessment Continuous assessment (one written summary of a reading assignment 25%, selected marked tutorial problems 25%, one oral examination on a topic from the course 50%).

PH5015 Experimental Quantum Physics at the Limit Semester: 1 Available: every second year; next in 2007-08 Credits:15 Number of lectures: 27 Lecturer: Professor Kishan Dholakia Overview

Quantum mechanics remains one of the most powerful but one of the least understood theories in physics. Typically students gain a good grounding in the theoretical and philosophical aspects of this topic but relatively little exposure to how quantum physics may be implemented in the laboratory and how important key applications are likely to be in future. The aim of the course is to build upon students’ knowledge of quantum physics and atomic physics to demonstrate how we can perform quantum mechanics on atoms, ions and photons in the laboratory. Learning outcomes Detailed understanding of laser cooling and Bose-Einstein condensation, Fermi gas production. Experimental tests of quantum mechanics in quantum gases. Laser cooling of ions. Understanding of the latest experimental techniques to develop cold quantum gases. Students will also gain a detailed knowledge of photon statistics and observations of non-classical light, quantum cryptography, single photon sources and quantum computers. Synopsis of course The course begins with discussion of laser cooling and Bose-Einstein condensation (BEC) explaining basic laser cooling, Doppler theory, sub Doppler cooling, magneto-optical traps. Quantum mechanical complementarity (which-way experiments). Evaporative cooling, magnetic trapping. Signatures of BEC and Fermi gases. Matter wave interference. Wave-particle duality studies. Charged ion trapping. Studies of laser cooled ions in traps. Quantum jumps. Atom lasers. Statistics of light: coherence. First and second order correlation functions. Chaotic light, coherent light. Photon statistics. Sub and super Poissonian light. Photon bunching and anti-bunching. Quantum cryptography. Entangled states. Single photon sources. Recommended books Haken and Wolf, The Physics of Atoms, fourth edition, Springer Verlag Thorne, Spectrophysics: principles and applications, Springer-Verlag Harold J. Metcalf and Peter van der Straten , Laser cooling and trapping, Springer Verlag Pethick, Bose-Einstein condensation, Cambridge Assessment A two hour examination = 75%. An assessed essay allowing students to read research papers and write an essay on a topic covered or linked closely in the course = 25%.

PH5016 Biophotonics Semester: 1 Available: every second year; due to be given next in 2006-07 Credits: 15 Number of lectures: 18 (+ Essay, Presentation, Group project) Lecturers: Prof T F Krauss, Prof K Dholakia and guest lecturers Overview The union of photonics and biotechnology presents some of the most exciting scientific and commercial prospects for the 21st century. Largely due to advances in microscopy and the invention of the laser in the 1960s, photonics has touched all aspects of our lives, ranging from home entertainment to optical telecommunications and data storage. Biophotonics is the fusion of photonics and biology that deals with the interaction between light and biological matter. Light is one of the primary tools in biology, and increasingly sophisticated optical instrumentation is used in biological detection and analysis as well as medical treatment. Aims and Objectives The module will expose students to the exciting opportunities offered by applying photonics methods and technology to biomedical sensing and detection. A rudimentary biological background will be provided where needed. Topics include fluorescence microscopy and assays, including time-resolved applications, optical tweezers for cell sorting and DNA manipulation, photodynamic therapy, lab-on-a-chip concepts and bio-MEMS. Learning Outcomes Students will gain an understanding of * Basic biological and biochemical concepts, such as the structure and function of cells, proteins and DNA. * The nature of the interaction between biological materials (cells, tissue etc.) with light, such as scattering, absorption and fluorescence. * Optical instrumentation used in biomedical practice. * Operation of biomedical detection systems such as assays and their detection limits. *Advanced optical techniques such as optical tweezers and the added functionality and information provided by these methods. Students will also gain transferable skills by developing some of the material themselves via critical study of research papers and materials, presentations and group work.

Synopsis Overview of Microscopy and relevance for biological inspection. Basics of Cell Biology, structure and function and cells. Optical scattering and absorption. Proteins and their use in assays. The nature of antibodies/antigens and their mutual binding mechanism. Fluorescent labels, fluorescence microscopy and related techhniques used in biomedical detection, including time-resolved methods. DNA, structure, use in assays, DNA microarrays. Operational principle of optical tweezers. Cell and DNA manipulation. Different types of beams, how they are generated and their applications. Manipulation and sorting of cells. Lab on a chip. Operation principle, microfabrication, microfluidics. Photodynamic therapy. Interaction of light and tissue. Different signatures of cancer and other abnormalities. Different types of light sources used and their respective advantages and effects, including time-resolved methods/short-pulse lasers. Prerequisites The course assumes a basic understanding of lasers and optics, as provided in either PH3010 (Modern Optics) or PH4034 (Laser Physics I). Recommended books The principal text is Introduction to Biophotonics by P.N.Prasad (Wiley, 2003, £58). Less relevant, but useful as a complementary text is Biophysics--an introduction by R. Cotterill (Wiley, 2002, approx £30). Presentation The module is intended to be very interactive, with group work, essays and student presentations supporting the lectures. Assessment 2-hour examination = 75%, continuous assessment = 25%.

PH5101 Project in Physics 2 Semester: whole year Available each year

Credits: 60 Overview The project aims to develop students’ skills in searching the physics literature, in experimental and observational design, the evaluation and interpretation of data, and the presentation of results. The main project is preceded by a review essay on a topic which may be related to the theme of the project or may be unrelated to it. There is no specific syllabus for this module. Students taking the MPhys degree select a project from a list of those available and are supervised by a member of the academic staff. Assessment Project and oral examination = 100%

PH5102 Project in Theoretical Physics Semester: whole year Available each year Credits: 45 Overview The project aims to survey the literature associated with the topic of the project and either(i) conduct original research into some problem in this field or (ii) prepare a research review of th field. There is no specific syllabus for this module. Students taking the MPhys degree select a project from a list of those available and are supervised by a member of the academic staff. Assessment Project and oral examination = 100%