What is “waving” for matter waves?bogner/isp209s9/lectures/l18p.pdf · What is “waving” for matter waves? ... There are two versions If the position of a proton, mass 1.67E-27

ISP209s9 Lecture 18 -1-

Today

• HW 7 and Exam 2 due Thurs. 8pm

• 10 min recap from last lecture on QM

• Finish QM odds and ends from ch.14

• The Standard Model

– 4 forces of Nature

– Fundamental particles of Nature

– Feynman diagrams


Wave-Matter Duality

• EM waves are waves in

EM fields

• EM waves interfere

• EM waves are quantized

Efield = 0,1hf, 2hf, 3hf,…

• “quanta” are photons

Ephoton = hf

• Quantum non-locality

• Matter waves are waves in

matter fields

• Matter waves interfere

• Matter waves are quantized

Efield = 0, mc2, 2mc2, …

• “quanta” are the particles

(e.g., electrons)

• Quantum non-locality


Quantum Non-Locality

Spread out EM field instantaneously “knows” it has lost 1hf of

energy when the photon impacts the screen at a distant point.

Einstein was

troubled!

“Spooky action

at a distance”


What is “waving” for matter waves?

• Probability – all particles described by a “wave

function” !. The square of ! gives the probability

density of finding a particle per unit volume.

• The ! extends over all space, which gives weird

consequences.

= prob. of finding particle in a small

volume V centered at the point r.


Observation can alter the outcome in QM

Electrons show an interference pattern in the double slit experiment.


Now try to watch which path the e- took

A watched electron doesn’t show interference!

If you try to find out

Which slit the electron

Goes thru, the wave features

Go away

An electron

Detector

Many more weird examples…


Quantum Tunneling

Particle bouncing

around in a box

Classically: A low energy particle does not

Escape the box. It is always inside.

Quantum Theory: The ! function extends

over all space, even outside the box. There

Is a finite probability the particle will

“tunnel” thru the box and found outside.

This is why some nuclei can radioactively

decay.


Quantization of Energy Levels in Atoms

Electrons in atoms can only assume discrete,

quantized values of Energy.

Ground state

1st excited state

2nd excited state


Lasers

E1

E2

Etc…

• Say you have many identical atoms that are all in the excited

state.

• You can set off a “chain reaction” where many of them

de-excite together, and the emitted photons stimulate the

de-excitation in the other atoms that releases still more photons.

Light Amplified Stimulated Emission


Bosons and Fermions

• Particles come in two types

• Bosons have the property that they canoverlap. Examples are photons and certainatoms (helium). They are social.

• Fermions can not exist in the same state. Theyare anti-social. Examples – electrons, protons.

• The fermion nature of electrons explainsatomic structure (periodic table and all that)


Heisenberg’s Uncertainty Principle

• Uncertainty Principle: It is not possible to know

exactly the position and momentum of a particle at

the same time.

• There is no absolute knowledge. The Newtonian

view of the world (if everything were known,

everything could be predicted) in not attainable.


Uncertainty depends on mass

electron

velocity

position

proton

baseball, highly

exaggerated (by

1025)


Sample Problem

!4

hpx "##

!4

htE "##

There are two versions

If the position of a proton, mass 1.67E-27 kg, is known to 1E-9 m the

momentum and velocity could have a range of

smkg

m

Js

x

hp

!!=

!

!=

"#"

$

$

$26

9

34

1027.51000.14

10625.6

4 %%

sm

kg

smkg

smkg

mp

6.311067.1

1027.5

v

1027.5v

27

26

26

=!

!!

="

!!="="

#

#

#


Quantum Nonlocality

1

2

1

2

After interaction the wave functions are

entangled.

If we measure 1 and 2 at the same time the

difference in position forms an interference

pattern.

If we measure 2 before 1, the measurement

of 2 defines where 1 must hit. This

information travels faster than the speed of

light.

This has been confirmed experimentally.

Interaction


From large to small

AtomsAtomic

NucleusA proton (uud)

Made of nuclei and

electrons. Size: 10-9m

Made of neutrons and

proton. Size 10-14 m

Made of quarks:

Size 10-15 m

A neutron has

dduISP209s9 Lecture 18 -16-

There are two more forces in nature – Strong Force

Strong force

– A force that exists between quarks, which have a property called colorcharge.

– The carrier of the force is the gluon (the gluon also has color charge)

– No isolated quarks are found in nature

– The force between protons-proton, protons-neutrons, and neutrons-neutrons is the result of the exchange of pairs of quarks. Pairs of quarksare called mesons (the pion is the lightest meson)

– The Strong force is responsible for binding atomic nuclei.


The Weak Force

Weak force

• A force between electrons, neutrinos and

protons (or neutrons), due to a property of

matter called weak charge.

• The carrier of the force are called weak vector

bosons W+ or W-, Z. The + or – tells the

electric charge of the boson.

• This force allows a neutron to change into a

proton and is responsible for most radioactive

decays.


Weak Potential

2 4 6 8 10DistanceHamL1

2

3

4

5

6

7

Weak Potential

The weak force falls off faster than 1/r2 .

Remember, the slope gives the magnitude of

the field (force).

distancequark quark

Electric potential shape - 1/r

Weak potential


A big picture

• Forces come about because of some

property of matter (charge, mass, weak

charge, color charge)

• The force is due to the exchange of “force

carrier” particles (photon, graviton, vector

boson, gluon)


The particles of nature

T. Kondo

-1

-1/3

+2/3

0

-1

Charge

(e)

00W-

1/30d

1/30u

01"

01e

Baryon

number

Lepton

number

Type

Quantum Numbers


Antiparticles

Every particle has a corresponding antiparticle. When a particle and an

anti particle meet they annihilate giving off energy. The fraction of

mass converted to energy in a matter anti-matter annihilation is 1, that

is, all the mass is converted to energy.

• A particle and its antiparticle have opposite values for all quantum

numbers except spin and mass.

• Example: The antiparticle of an electron is a positron. In all other

cases, the name of the antiparticle is anti- in front of the name of the

particle, such as proton and anti-proton.

• Antiparticles are written with a line over the top: p vs p (the

antiproton)


Antimatter

• Antimatter (matter made of anti-particles) is very difficult to

make. It can artificially be produced only at large particle

accelerators (“atom smashers”).

• Matter and anti-matter are created naturally in pairs

• So far the total amount of antimatter ever produced by

humankind is a few grams, and that almost immediately

annihilated with matter.

• The total energy in 1 g of anti-matter is:

E=mc2 = 0.001kg (3E8)2=9E14 J = 9E5 GJ

enough to run a normal power plant for 1 day.


Neutrinos

• Subatomic particles that do not have charge, but interactvia the weak force.

• These are very unusual particles and we still don’t knowmuch about their properties. They have a mass, but it is sosmall we have not been able to measure it.

• They come in three types, but the types mix.

• They account for about 2% of the universe but interactweakly. One light-year of lead would have only a 50%chance of stopping one.


Observatories for neutrinos

Sudbury solar neutrino

detector


A way to picture forces – Feynman Diagrams

quarkquark

g


Alternative version of the uncertainty principle

Time and energy also also related.

!4

htE "##

!4

hpx "##

It is possible for a short time to get something for nothing. But, it

has to be paid back.

On the very small scale, empty space is alive with “fluctuations”.

Particles can pop into and out of existence.


Quantum Chromo Dynamics - QCD

Feynman Diagram for the Strong force

Looks

like

This is called an exchange

force. The probability of an

interaction decreases

exponentially with the mass

of the exchanges particle.

Exponentially means, twice

the mass is e2=7.3 times less

space

tim

e

The more massive the particle exchanged, the shorter the range

of the force.ISP209s9 Lecture 18 -28-

The problem with QCD

Gluons themselves have color charge!

“normal” This is also possible.


Equations – sort of

Rules for Feynman Diagrams:

1). The number of leptons and baryons must be conserved.

2). Charge must be conserved.

Not

allowed

since lepton

number not

conserved

allowed


A summary of the forces of nature

infiniteGraviton (?)6x10-39Gravity

10-18

Only 0.001 width

of proton

Vector Bosons W+, W-, Z010-6Weak

infinitephoton1/137Electromagnetic

10-15 size of a

proton

Gluon, g, between quarks

Mesons-protons/neutrons

1Strong

Range (m)CarrierStrengthForce


Back to the weak and electromagnetic forces

Transformation of a neutron into a

proton by an interaction with a neutrino

via the Weak force.

(udd)

neutron

proton

(udu)

W-

e

electron

"

neutrino

e e

e e

photon

In the process: Energy (including mass); momentum,

charge, baryon number, lepton number, are conserved.

Repulsive force between two

electrons.


Quantum Electrodynamics - QED

• The description of the forces on the previous page is based on atheory called quantum electrodynamics.

• Most successful theory every devised – it has at the moment noknown problems and describes all electric, magnetic and weakinteractions.

• Strength of the EM force:

• Unification of EM and Weak Forces is called Electroweak theory

• Theory of the strong force is called Quantum Chromodynamics

experiment)32(03599979.137

1

theory)56(03599941.137

1

=

=

!

!

Documents

What is “waving” for matter waves?bogner/isp209s9/lectures/l18p.pdf · What is “waving” for matter waves? ... There are two versions If the position of a proton, mass 1.67E-27