Quantum Mechanics Solution Manual
© Leon van Dommelen
Next:
A.1 Classical Lagrangian mechanics
A. Addenda
Subsections
A.
1
Classical Lagrangian mechanics
A.
1
.
1
Introduction
A.
1
.
2
Generalized coordinates
A.
1
.
3
Lagrangian equations of motion
A.
1
.
4
Hamiltonian dynamics
A.
1
.
5
Fields
A.
2
An example of variational calculus
A.
3
Galilean transformation
A.
4
More on index notation
A.
5
The reduced mass
A.
6
Constant spherical potentials
A.
6
.
1
The eigenvalue problem
A.
6
.
2
The eigenfunctions
A.
6
.
3
About free space solutions
A.
7
Accuracy of the variational method
A.
8
Positive ground state wave function
A.
9
Wave function symmetries
A.
10
Spin inner product
A.
11
Thermoelectric effects
A.
11
.
1
Peltier and Seebeck coefficient ballparks
A.
11
.
2
Figure of merit
A.
11
.
3
Physical Seebeck mechanism
A.
11
.
4
Full thermoelectric equations
A.
11
.
5
Charge locations in thermoelectrics
A.
11
.
6
Kelvin relationships
A.
12
Heisenberg picture
A.
13
Integral Schrödinger equation
A.
14
The Klein-Gordon equation
A.
15
Quantum Field Theory in a Nanoshell
A.
15
.
1
Occupation numbers
A.
15
.
2
Creation and annihilation operators
A.
15
.
3
The caHermitians
A.
15
.
4
Recasting a Hamiltonian as a quantum field one
A.
15
.
5
The harmonic oscillator as a boson system
A.
15
.
6
Canonical (second) quantization
A.
15
.
7
Spin as a fermion system
A.
15
.
8
More single particle states
A.
15
.
9
Field operators
A.
15
.
10
Nonrelativistic quantum field theory
A.
16
The adiabatic theorem
A.
17
The virial theorem
A.
18
The energy-time uncertainty relationship
A.
19
Conservation Laws and Symmetries
A.
19
.
1
An example symmetry transformation
A.
19
.
2
Physical description of a symmetry
A.
19
.
3
Derivation of the conservation law
A.
19
.
4
Other symmetries
A.
19
.
5
A gauge symmetry and conservation of charge
A.
19
.
6
Reservations about time shift symmetry
A.
20
Angular momentum of vector particles
A.
21
Photon type 2 wave function
A.
21
.
1
The wave function
A.
21
.
2
Simplifying the wave function
A.
21
.
3
Photon spin
A.
21
.
4
Energy eigenstates
A.
21
.
5
Normalization of the wave function
A.
21
.
6
States of definite linear momentum
A.
21
.
7
States of definite angular momentum
A.
22
Forces by particle exchange
A.
22
.
1
Classical selectostatics
A.
22
.
2
Classical selectodynamics
A.
22
.
3
Quantum selectostatics
A.
22
.
4
Poincaré and Einstein try to save the universe
A.
22
.
5
Lorenz saves the universe
A.
22
.
6
Gupta-Bleuler condition
A.
22
.
7
The conventional Lagrangian
A.
22
.
8
Quantization following Fermi
A.
22
.
9
The Coulomb potential and the speed of light
A.
23
Quantization of radiation
A.
23
.
1
Properties of classical electromagnetic fields
A.
23
.
2
Photon wave functions
A.
23
.
3
The electromagnetic operators
A.
23
.
4
Properties of the observable electromagnetic field
A.
24
Quantum spontaneous emission
A.
25
Multipole transitions
A.
25
.
1
Approximate Hamiltonian
A.
25
.
2
Approximate multipole matrix elements
A.
25
.
3
Corrected multipole matrix elements
A.
25
.
4
Matrix element ballparks
A.
25
.
5
Selection rules
A.
25
.
6
Ballpark decay rates
A.
25
.
7
Wave functions of definite angular momentum
A.
25
.
8
Weisskopf and Moszkowski estimates
A.
25
.
9
Errors in other sources
A.
26
Fourier inversion theorem and Parseval
A.
27
Details of the animations
A.
28
WKB Theory of Nearly Classical Motion
A.
28
.
1
Solution wkb-a
A.
28
.
2
Solution wkb-b
A.
29
WKB solution near the turning points
A.
30
Three-dimensional scattering
A.
30
.
1
Partial wave analysis
A.
30
.
2
Partial wave amplitude
A.
30
.
3
The Born approximation
A.
31
The Born series
A.
32
The evolution of probability
A.
33
Explanation of the London forces
A.
34
Explanation of Hund’s first rule
A.
35
The third law
A.
36
Alternate Dirac equations
A.
37
Maxwell’s wave equations
A.
38
Perturbation Theory
A.
38
.
1
Basic perturbation theory
A.
38
.
2
Ionization energy of helium
A.
38
.
3
Degenerate perturbation theory
A.
38
.
4
The Zeeman effect
A.
38
.
5
The Stark effect
A.
39
The relativistic hydrogen atom
A.
39
.
1
Introduction
A.
39
.
2
Fine structure
A.
39
.
3
Weak and intermediate Zeeman effect
A.
39
.
4
Lamb shift
A.
39
.
5
Hyperfine splitting
A.
40
Deuteron wave function
A.
41
Deuteron model
A.
41
.
1
The model
A.
41
.
2
The repulsive core
A.
41
.
3
Spin dependence
A.
41
.
4
Noncentral force
A.
41
.
5
Spin-orbit interaction
A.
42
Nuclear forces
A.
42
.
1
Basic Yukawa potential
A.
42
.
2
OPEP potential
A.
42
.
3
Explanation of the OPEP potential
A.
42
.
4
Multiple pion exchange and such
A.
43
Classical vibrating drop
A.
43
.
1
Basic definitions
A.
43
.
2
Kinetic energy
A.
43
.
3
Energy due to surface tension
A.
43
.
4
Energy due to Coulomb repulsion
A.
43
.
5
Frequency of vibration
A.
44
Relativistic neutrinos
A.
45
Fermi theory
A.
45
.
1
Form of the wave function
A.
45
.
2
Source of the decay
A.
45
.
3
Allowed or forbidden
A.
45
.
4
The nuclear operator
A.
45
.
5
Fermi’s golden rule
A.
45
.
6
Mopping up
A.
45
.
7
Electron capture
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A.1 Classical Lagrangian mechanics
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