Paul
E.
Dimotakis
Lectures
on
Quantum
Physics
and
Rppl
icat
ions
@
1980,
by
the
author.
Caliqornia
Institute
of
Technology
Contents
Page
1
CONTENTS
1.
CLRSSICRL
MECHANICS......
.............................
1.1
1.1
The
principle
of
stationary
action
Lagr
ang
i
an
bal
1
istic
trajectory
one-dimensional harmonic
osci
1
lator
motion
of
gravitating
pair
motion
in
two-dimensional
potential
momentum
mot
ion
in
an
Electromagnetic
f
ield
1.2
Conservation
laws
Momentum
Energy
1.3
Hamtltonian
1.4
Poisson
brackets
and
constants
of
the
motion
1.5
The
assumptions
of classical
mechanics
References
Problems
2.
WAVE
MECHRNICS
.............................................
2.1
2.1
An
interference
expertment
2.2
Wave
packets
Four
~er
transform
Parseual
's
theorem
Expectatton
values
x.
k operators
Local
tzat
on
M~n~mum
joint
spread
Nave
packets
of definite
x,
or
k
Commuting
operators
&
simultaneous
localnzation
Localization
In
three
dtmensions
Wave
packet
motion.
Phase
&
group
velocity
Frequency
&
time
2.3
Energy
and
momentum
Black
body
radiation
Photoelectric
effect
Compton
scattering
UeBroglre
thesis
Momentum
and
energy
operators
2.4
Wave
parttcle
duality
and
the
uncertainty
principle
2.5
Summary
an0
conclusions.
The
correspondence
prtnciple
References
Problems
3.
THE
SCHRODINGER
EQURTION.....................................
3.1
3.1 Hermttian operators.
Eigenfunctions
&
eigenvalues
3.1
momentum
3.1
adjoint
operator
3.2
real
elgenvalues
3.5
orthogonal
eigenfunctions
3.6
min
imum/max
tmum
expectat
ton
values
3.7
3.2
Superposition
of
eigenfunctions
3.8
June
13,
1980
Contents
Page
2
3.3
Eigenfunction
expansions.
Completeness.
3.10
3.4
Hermitian operators
and
associated
obleruables
3.13
3.5
The
energy
operator.
Schrodinger equation.
3.15
Time
rate of
change
of
an
operator,
Constants
of
the
motion
3.17
Conseruat
ion
of
probab
i
l
i
ty
3.19
References
Problems
4.
QUANTUM
BEHAVIOR
IN
ONE-DIMENSIONAL
POTENTIRLS...............
4.1
4.1
Matchlng
cond~t
Ions
4.3
4.2
motion
~n
a
constant
potentlal.
Free
partzcle
Oehaulor
4.5
4.2.1
Scattering
by
a
potentla1
step
4.6
4.2.2
Scatterlng
by
a
potentlal
step
of
flnlte
length
4.10
4.2.3
Tunnel~ng
4.14
4.2.4
Bound
states
of
a
rectangular
potentad1
well
4.16
4.2.5
The
lnf~nlte
potentral
well
4.23
4.3
Denslty
of
states
4.215
4.3.1
Mot~on
an
one
dimension
4.25
4.3.2
Per
iodlc
boundary
cond~trons
4.27
4.3.3
Density
of
states
in
tnree
dlmenslons
4.28
4.3.4
Fermx
energy
of
conduction
electrons
zn
a
metal
4.32
4.3.5
F~eld
emiss~on
4.34
4.3.6
Contact
potentials
4.37
4.3.7
Paramagnetzc
OehaUlOr
of
metals
4.38
References
Problems
3.
HRRMONIC
OSCILLATOR
SYSTEMS..................................
5.1
5.1
Elgenualues
and
elgenfunctions
5.2
5.2
Ladder
operators
5.3
5.3
Harmonic
oscl
l
lators
In
thermal
equl
l
lbrlum
5.7
5.4
systems
of
uncoupled
harmonlc
osc~l~ators
5.8
5.5
systems
of
uncoupled
harmonlc
oscrllators
in
thermal
equlltbr~um
5.11
5.6
Quantum
mechan~cs
of
a
fluid.
Phonons.
5.13
Problems
6.
ORBITAL
ANGULAR
MOMENTUM.....................................
6.1
6.1
The
two
dimensional
harmonic
oscillator
6.1
Circular
quanta
6.3
Motionof
achargedparticle
in
auniformmagnetic
6.6
field
6.2
Angular
momentum
in
three
dimensions
6.8
Rotational
spectra
of
diatomic
molecules
at
IOU
temperatures
6.15
6.3
The
spherical
harmonics
6.18
Problems
June
13,
1980
Contents
Page
3
7.
MOTION
IN
A
CENTRAL
POTENTIAL...........................
....
7.1
7.1
Motion
in
a
constant
potential.
Free
particle
motion
in
spherical
coordinates
7.4
7.2
Bound
states
of
the spherical
potential
uell
7.6
7.3
Motion
in
an
attractive
Coulomb
potential.
Hydrogenic
uauefunctions
7.9
7.4
Vibrational-Rotational spectra
of
diatomic
molecules
7.16
7.4.1
Diatomic molecules
in
thermal
equilibrium
7.23
7.4.2
Radiative
transitions
of
diatomic
molecules
in
thermal
equilibrium
7.27
Problems
.
METHODS
OF
APPROXIM~TION......................................
8.1
8.1
Time-independent
perturtaatzon
of
non-degenerate
states
8.5
Polarrzabil~ty
of
harmonrcally
bound
charge
8.
11
Special
techniques
(auxllrary
operatorsr
sum
rules)
8.15
Polarrzabrllty
of
hydrogen
atom
ground
state
8.15
fin
rmproued
perturbat
ron
expans
ton
8.17
8.2
Perturbat
ron
of
nearly
degenerate
states
8.19
8.3
Perturbat
ran
of
degenerate
states
8.23
The
lrnear
Stark
effect
8.23
8.4
Time
dependent
perturbatron
theory
8.26
Flrst
Born
approximation
8.27
Impulsrve
start
of
a
constant
potential
8.28
Transltlon
amp]
ltude
matrrx
8.28
8.4.1
Unltarrty
and
the
conservatron
of
probability
8.32
8.4.2
Transttions
as
a
result of
perturbat~ons
locallzed
rn
tame.
The
S-matrlx.
8.
33
Response
of
a
ground
state
charged
part
lcle
harmonic
oscll
lator
to
a
Gaussran
tmpulse
electric
f
leld
8.34
8.4.3
Transzt~ons
as
a
result
of
harmonlc
perturbat~ons
8.36
Transrslons
to
or
from
a
continuum
8. 38
8.4.4
The
d~fferenttai
scattering
cross-sectlon
in
the
Born
approxrmat~on
8.39
Coulomb
Scattering
8.41
8.5
Transitions
and
the
superposltron
of
pure
energy
states
8.42
8.6
An
rmproued
transrtlon
rate
calculation
8.47
Prob
1
ems
9.1
THE
ELECTROMAGNETIC
FIELD...................................
9.1
The
Hamiltonian
Transition
to
Quantum
Mechanics
The
Quantum
Mechanical
vector
potential
operator
The
ground
state
of
the
electromagnetic
field
The
electromagnetic
field in
thermal
equilibrium.
Black
body
radiation.
The
eigenstates
of
the
electromagnetic
field
Electromagnetic
field
momentum
The
photon
Photons
and
uaue-particle
dual
ity
The
angular
momentum
of
the
photon
The
vector
potential
in
terms
of circular
polarization
operators
Photon
modes
June
13,
1980