Practical Quantum Mechanics

Original title page
Volume I:
I. General Concepts
1. Law of probability conservation
2. Variational principle of Schrödinger
3. Classical mechanics for space averages
4. Classical laws for angular motion
5. Energy conservation law
6. Hermitian conjugate
7. Construction of an hermitian operator
8. Derivatives of an operator
9. Time rate of an expectation value
10. Schrödinger and Heisenberg representations
11. Time dependent hamiltonian
12. Repeated measurement
13. Curvilinear coordinates
14. Momentum space wave functions
15. Momentum space: Periodic and aperiodic wave functions
II. One-Body Problems without Spin
A. One-Dimensional Problems
16. Force-free case: Basic solutions
17. Force-free case: Wave packet
18. Standing wave
19. Opaque division wall
20. Opaque wall described by Dirac δ function
21. Scattering at a Dirac δ function wall
22. Scattering at a symmetric potential barrier
23. Reflection at a rectangular barrier
24. Inversion of reflection
25. Rectangular potential hole
26. Rectangular potential hole between two walls
27. Virtuallevels
28. Periodic potential
29. Dirac comb
30. Harmonic oscillator
31. Oscillator in Hilbert space
32. Oscillator eigenfunctions constructed by Hilbert space operators
33. Harmonic oscillator in matrix notation
34. Momentum space wave functions of oscillator
35. Anharmonic oscillator
36. Approximate wave functions
37. Potential step
38. Pöschl-Teller potential hole
39. Potential hole of modified Pöschl-Teller type
40. Free fall of a body over earth's surface
41. Accelerating electrical field
B. Problems of Two or Three Degrees of Freedom without Spherical Symmetry
42. Circular oscillator
43. Stark effect of a two-dimensional rotator
44. Ionized hydrogen Molecule
45. Oblique incidence of a plane wave
46. Symmetrical top
C. The Angular Momentum
47. Infinitesimal rotation
48. Components in polar coordinates
49. Angular momentum and Laplacian
50. Hilbert space transformations
51. Commutators in Schrôdinger representation
52. Particles of spin 1
53. Commutation with a tensor
54. Quadrupole tensor. Spherical harmonics
55. Transformation of spherical harmonics
56. Construction of Hilbert space for an angular momentum component
57. Orthogonality of spherical harmonics
D. Potentials of Spherical Symmetry
a) Bound States
58. Angular momentum expectation values
59. Construction of radial momentum operator
60. Solutions neighbouring eigenfunctions
61. Quadrupole moment
62. Particle enclosed in a sphere
63. Square well of finite depth
64. Wood-Saxon potential
65. Spherical oscillator
66. Degeneracy of the spherical oscillator
67. Kepler problem
68. Hulthén potential
69. Kratzer's molecular potential
70. Morse potential
71. Rotation correction of Morse formula
72. Yukawa potential hole
73. Isotope shift in x-rays
74. Muonic atom ground state
75. Central-force model of deuteron
76. Momentum space wave functions for central force potentials
77. Momentum space integral equation for central force potentials
78. Momentum space wave functions for hydrogen
79. Stark effect of a three-dimensional rotator
b) Problems of Elastic Scattering
80. Interference of incident and scattered waves
81. Partial wave expansion of plane wave
82. Partial wave expansion of scattering amplitude
83. Scattering at low energies
84. Scattering by a constant repulsive potential
85. Anomalous scattering
86. Scattering resonances
87. Contribution of higher angular momenta
88. Shape-independent approximation
89. Rectangular hole: Low-energy scattering
90. Low-energy scattering and bound state
91. Deuteron potential with and without hard core
92. Low-energy cross section with and without hard core
93. Low-energy scattering by a modified Pöschl-Teller potential hole
94. Radial Integral equation
95. Variational principle of Schwinger
96. Successive approximations to partial-wave phase shift
97. Calogero's equation
98. Linearization of Calogero's equation
99. Scattering length for a negative-power potential
100. Second approximation to Calogero equation
101. Square-well potential: Scattering length
102. Scattering length for a Yukawa potential
103. Improvement of convergence in a spherical harmonies series
104. Collision-parameter integral
105. Born scattering: Successive approximation steps
106. Scattering by a Yukawa potential
107. Scattering by an exponential potential
108. Born scattering by a charge distribution of spherical ymmetry
109. Hard sphere: High energy scattering
110. Rutherford scattering formula
111. Partial wave expansion for the Coulomb field
114. Anomalous scattering
113. Sommerfeld-Watson transform
114. Regge pole
E. The Wentzel-Kramers-Brillouin (WKB) Approximation
115. Eikonal expansion
116. Radial WKB solutions
117. WKB boundary condition of Langer
118. Oscillator according ta WKB approach
119. WKB eigenvalues in a homogeneous field
120. Kepler problem in WKB approach
121. WKB phases in the force-free case
122. Calculation of WKB phases
123. Coulomb phases by WKB method
124. Quasipotential
F. The Magnetic Field
125. Introduction of a magnetic field
126. Current in presence of a magnetic field
127. Normal Zeeman effect
128. Paramagnetic and diamagnetic susceptibilities without spin
Volume II:
III. Particles with Spin
A. One-Body Problems
129. Construction of Pauli matrices
130. Eigenstates of Pauli matrices
131. Spin algebra
132. Spinor transformation properties
133. Spin electron in a central field
134. Quadrupole moment of a spin state
135. Expectation values of magnetic moments
136. Fine structure
137. Plane wave of spin t particles
138. Free electron spin resonance
B. Two- and Three-Body Problems
139. Spin functions for two particles
140. Spin-dependent central force between nucleons
141. Powers of spin operators
142. Angular momentum eigenfunctions of two spin particles
143. Tensor force operator
144. Deuteron with tensor interaction
145. Electrical quadrupole and magnetic dipole moments of deuteron
146. Spin functions of three particles
147. Neutron scattering by molecular hydrogen
IV. Many-Body Problems
A. Few Particles
148. Two repulsive particles on a circle
149. Three-atomic linear molecule
150. Centre-of-mass motion
151. Virial theorem
152. Slater determinant
153. Exchange in interaction terms with Slater determinant
154. Two electrons in the atomic ground state
155. Excited states of the helium atom
156. Excited S states of the helium atom
157. Lithium ground state
158. Exchange correction to lithium ground state
159. Dielectric susceptibility
160. Diamagnetic susceptibility of neon
161. Van der Waals attraction
162. Excitation degeneracy
163. Neutral hydrogen molecule
164. Scattering of equal particles
165. Anomalous proton-proton scattering
166. Inelastic scattering
B. Very Many Particles: Quantum Statistics
167. Electron gas in a metal
168. Paramagnetic susceptibility of a metal
169. Field emission, uncorrected for image force
170. Field emission, corrected for image force
171. White dwarf
172. Thomas-Fermi approximation
173. Amaldi correction for a neutral atom
174. Energy of a Thomas-Fermi atom
175. Virial theorem for the Thomas-Fermi atom
176. Tietz approximation of a Thomas-Fermi field
177. Variational approximation of Thomas-Fermi field
178. Screening of K electrons
V. Non-Stationary Problems
179. Two-Ievel system with time-independent perturbation
180. Periodic perturbation of two-Ievel system
181. Dirac perturbation method
182. Periodic perturbation: Resonance
183. Golden Rule for scattering
184. Born scattering in momentum space
185. Coulomb excitation of an atom
186. Photoeffect
187. Dispersion of light. Oscillator strengths
188. Spin flip in a magnetic resonance device
VI. The Relativistic Dirac Equation
189. Iteration of the Dirac equation
190. Plane Dirac waves of positive energy
191. Transformation properties of a spinor
192. Lorentz covariants
193. Parity transformation
194. Charge conjugation
195. Mixed helicity states
196. Spin expectation value
197. Algebraic properties of a Dirac wave spinor
198. Current in algebraic formulation
199. Conduction current and polarization current
200. Splitting up of Dirac equations into two pairs
201. Central forces in Dirac theory
202. Kepler problem in Dirac theory
203. Hydrogen atom fine structure
204. Radial Kepler solutions at positive kinetic energies
205. Angular momentum expansion of plane Dirac wave
206. Scattering by a central force potential
207. Continuous potential step
208. Plane wave at a potential jump
209. Reflected intensity at a potential jump
VII. Radiation Theory
210. Quantization of schrödinger field
211. Scattering in Born approximation
212. Quantization of classical radiation field
213. Emission probability of a photon
214. Angular distribution of radiation
215. Transition probability
216. Selection rules for dipole radiation
217. Intensities of Lyman lines
218. Compton effect
219. Bremsstrahlung
Both volumes:
Mathematical Appendix
Coordinate systems
Γ function
Bessel functions
Legendre functions
Spherical harmonies
The hypergeometric series
The confluent series
Some functions defined by integrals
Index for Volumes 1 and II