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PHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and Waves X2X2 t=0 t final t final =(x 2 -x 1 )/v X1X1
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PHYSICAL CHEMISTRY - ADVANCED MATERIALSPHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and WavesParticles and Waves
Two opposing concepts
Particle theory
Field theory
Quantum Mechanics
Position, mass, velocity, charge, spin
Functions continuous in space and time
PHYSICAL CHEMISTRY - ADVANCED MATERIALSPHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and WavesParticles and Waves
X1 X2
t=0
t=0
tfinal
tfinal=(x2-x1)/vparticle
wave
Mechanical Analogy of transmision Mechanical Analogy of transmision
PHYSICAL CHEMISTRY - ADVANCED MATERIALSPHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and WavesParticles and Waves
X2
t=0
t=0
tfinal
tfinal=(x2-x1)/v
X1
PHYSICAL CHEMISTRY - ADVANCED MATERIALSPHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and WavesParticles and Waves
SImple Harmonic MotionSImple Harmonic Motion
m
)sin(2/1
2
2
tm
Ax
xdtxdm
dtdvmmaF
Equation of Motion Equation of Motion
Displacement Displacement x
PHYSICAL CHEMISTRY - ADVANCED MATERIALSPHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and WavesParticles and Waves
Wave: Wave: The propagation of a perturbation. It is also a way to transport Energy.Periodic changes in Space and Time of some Property.There is no net dosplacement of the medium
Shape of the disturbance: Shape of the disturbance:
„Profile“ of the wave such as an instantaneous „snapshot“ of the wave form.It reoeats periodically in Time and Space.Particular „Pattern“: Sinusoidal Waves. These waves are called „Harminic Waves“.
PHYSICAL CHEMISTRY - ADVANCED MATERIALSPHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and WavesParticles and Waves
One-Dimensional Waves – General ConceptsOne-Dimensional Waves – General Concepts
t o x
Shape of the disturbance Shape of the disturbance
Harmonic WavesHarmonic Waves→ → Sinusoidal WavesSinusoidal Waves
Time, t
T
Temporal Period Temporal Period ),(),( Ttxtx
Space, x
Spatial Period or WavelengthSpatial Period or Wavelength ),(),( txtx
PHYSICAL CHEMISTRY - ADVANCED MATERIALSPHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and WavesParticles and Waves
Space, x
p
AmplitudeAmplitude
PhasePhase
time, t
Ref
FrequencyFrequency
Tf 1
Angular FrequencyAngular Frequency
T
f
22
Wave NumberWave Number
1
Angular Wave NumberAngular Wave Numberor propagation Numberor propagation Number
2k
fT
v
Phase VelocityPhase VelocityTemporal PeriodTemporal Period
v
T
PHYSICAL CHEMISTRY - ADVANCED MATERIALSPHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and WavesParticles and Waves
)v(2sin
sin
22sinsin),(
txA
tkxA
tT
xAtkxAtx
Wave FunctionWave Function
Differential Wave EquationDifferential Wave Equation
2
2
22
2
v1
tx
PHYSICAL CHEMISTRY - ADVANCED MATERIALSPHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and WavesParticles and Waves
Travelling WavesTravelling Waves
)v(2sin txA
)v(2sin txA
PHYSICAL CHEMISTRY - ADVANCED MATERIALSPHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and WavesParticles and Waves
Travelling / Standing WavesTravelling / Standing Waves
)v(2sin1 txA
)v(2sin2 txA
txA
txtxA
v2cos2sin2
)v(2sin)v(2sin21
Standing Waves:Standing Waves: When the primary and reflected Waves have the same A and speed It vibrates „in place“.Nodes: Places where the medium does not ever vibrate.
PHYSICAL CHEMISTRY - ADVANCED MATERIALSPHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and WavesParticles and Waves
The Complex RepresentationThe Complex Representation
Complex number:Complex number: 1 with iiyxz
Imaginary y
Real x
|z|
(x+i y)
x=|z| cos y=|z| sin
Euler Formula:Euler Formula: z = |z| (cos + isin |z| ei
Complex Conjugate:Complex Conjugate: z* = |z| (cos - isin |z| e-i
Wave Function:Wave Function: )cos()( tkxAeA tkxi
PHYSICAL CHEMISTRY - ADVANCED MATERIALSPHYSICAL CHEMISTRY - ADVANCED MATERIALS Particles and WavesParticles and Waves
Light as an Electromagnetic WaveLight as an Electromagnetic Wave
+EE
Differential Wave EquationDifferential Wave Equation
2
2
22
2
2
2
22
2
c1c1
tB
xB
tE
xE