From the Preface to the first English edition xi
Preface to the second English edition xii
Preface to the third Russian edition xiii
Editor's Preface to the fourth Russian edition xiv
Notation xv
I. The Basic Concepts of Quantum Mechanics
1. The uncertainty principle 1
2. The principle of superposition 6
3. Operators 8
4. Addition and multiplication of operators 13
5. The continuous spectrum 15
6. The passage to the limiting case of classical mechanics 19
7. The wave function and measurements 21
II. Energy and Momentum
8. The Hamiltonian operator 25
9. The differentiation of operators with respect to time 26
10. Stationary states 27
11. Matrices 30
12. Transformation of matrices 35
13. The Heisenberg representation of operators 37
14. The density matrix 38
15. Momentum 41
16. Uncertainty relations 45
III. Schrodinger's Equation
17. Schrodinger's equation 50
18. The fundamental properties of Schrodinger's equation 53
19. The current density 55
20. The variational principle 58
21. General properties of motion in one dimension 60
22. The potential well 63
23. The linear oscillator 67
24. Motion in a homogeneous field 74
25. The transmission coefficient 76
IV. Angular Momentum
26. Angular momentum 82
27. Eigenvalues of the angular momentum 86
28. Eigenfunctions of the angular momentum 89
29. Matrix elements of vectors 92
30. Parity of a state 96
31. Addition of angular momenta 99
V. Motion in a Centrally Symmetric Field
32. Motion in a centrally symmetric field 102
33. Spherical waves 105
34. Resolution of a plane wave 112
35. Fall of a particle to the centre 114
36. Motion in a Coulomb field (spherical polar coordinates) 117
37. Motion in a Coulomb field (parabolic coordinates) 129
VI. Perturbation Theory
38. Perturbations independent of time 133
39. The secular equation 138
40. Perturbations depending on time 142
41. Transitions under a perturbation acting for a finite time 146
42. Transitions under the action of a periodic perturbation 151
43. Transitions in the continuous spectrum 154
44. The uncertainty relation for energy 157
45. Potential energy as a perturbation 159
VII. The Quasi-Classical Case
46. The wave function in the quasi-classical case 164
47. Boundary conditions in the quasi-classical case 167
48. Bohr and Sommerfeld's quantization rule 170
49. Quasi-classical motion in a centrally symmetric field 175
50. Penetration through a potential barrier 179
51. Calculation of the quasi-classical matrix elements 185
52. The transition probability in the quasi-classical case 191
53. Transitions under the action of adiabatic perturbations 195
VIII. Spin
54. Spin 199
55. The spin operator 203
56. Spinors 206
57. The wave functions of particles with arbitrary spin 210
58. The operator of finite rotations 215
59. Partial polarization of particles 221
60. Time reversal and Kramers' theorem 223
IX. Identity of Particles
61. The principle of indistinguishability of similar particles 227
62. Exchange interaction 230
63. Symmetry with respect to interchange 234
64. Second quantization. The case of Bose statistics 241
65. Second quantization. The case of Fermi statistics 247
X. The Atom
66. Atomic energy levels 251
67. Electron states in the atom 252
68. Hydrogen-like energy levels 256
69. The self-consistent field 257
70. The Thomas-Fermi equation 261
71. Wave functions of the outer electrons near the nucleus 266
72. Fine structure of atomic levels 267
73. The Mendeleev periodic system 271
74. X-ray terms 279
75. Multipole moments 281
76. An atom in an electric field 284
77. A hydrogen atom in an electric field 289
XI. The Diatomic Molecule
78. Electron terms in the diatomic molecule 300
79. The intersection of electron terms 302
80. The relation between molecular and atomic terms 305
81. Valency 309
82. Vibrational and rotational structures of singlet terms in the diatomic molecule 316
83. Multiplet terms. Case a 321
84. Multiplet terms. Case b 325
85. Multiplet terms. Cases c and d 329
86. Symmetry of molecular terms 331
87. Matrix elements for the diatomic molecule 334
88. A-doubling 338
89. The interaction of atoms at large distances 341
90. Pre-dissociation 344
XII. The Theory of Symmetry
91. Symmetry transformations 356
92. Transformation groups 359
93. Point groups 362
94. Representations of groups 370
95. Irreducible representations of point groups 378
96. Irreducible representations and the classification of terms 382
97. Selection rules for matrix elements 385
98. Continuous groups 389
99. Two-valued representations of finite point groups 393
XIII. Polyatomic Molecules
100. The classification of molecular vibrations 398
101. Vibrational energy levels 405
102. Stability of symmetrical configurations of the molecule 407
103. Quantization of the rotation of a top 412
104. The interaction between the vibrations and the rotation of the molecule 421
105. The classification of molecular terms 425
XIV. Addition of Angular Momenta
106. 3j-symbols 433
107. Matrix elements of tensors 441
108. 6j-symbols 444
109. Matrix elements for addition of angular momenta 450
110. Matrix elements for axially symmetric systems 452
XV. Motion in a Magnetic Field
111. Schrodinger's equation in a magnetic field 455
112. Motion in a uniform magnetic field 458
113. An atom in a magnetic field 463
114. Spin in a variable magnetic field 470
115. The current density in a magnetic field 472
XVI. Nuclear Structure
116. Isotopic invariance 474
117. Nuclear forces 478
118. The shell model 482
119. Non-spherical nuclei 491
120. Isotopic shift 496
121. Hyperfine structure of atomic levels 498
122. Hyperfine structure of molecular levels 501
XVII. Elastic Collisions
123. The general theory of scattering 504
124. An investigation of the general formula 508
125. The unitarity condition for scattering 511
126. Born's formula 515
127. The quasi-classical case 521
128. Analytical properties of the scattering amplitude 526
129. The dispersion relation 532
130. The scattering amplitude in the momentum representation 535
131. Scattering at high energies 538
132. The scattering of slow particles 545
133. Resonance scattering at low energies 552
134. Resonance at a quasi-discrete level 559
135. Rutherford's formula 564
136. The system of wave functions of the continuous spectrum 567
137. Collisions of like particles 571
138. Resonance scattering of charged particles 574
139. Elastic collisions between fast electrons and atoms 579
140. Scattering with spin-orbit interaction 583
141. Regge poles 589
XVIII. Inelastic Collisions
142. Elastic scattering in the presence of inelastic processes 595
143. Inelastic scattering of slow particles 601
144. The scattering matrix in the presence of reactions 603
145. Breit and Wigner's formulae 607
146. Interaction in the final state in reactions 615
147. Behaviour of cross-sections near the reaction threshold 618
148. Inelastic collisions between fast electrons and atoms 624
149. The effective retardation 633
150. Inelastic collisions between heavy particles and atoms 637
151. Scattering of neutrons 640
152. Inelastic scattering at high energies 644
Mathematical Appendices
a. Hermite polynomials 651
b. The Airy function 654
c. Legendre polynomials 656
d. The confluent hypergeometric function 659
e. The hypergeometric function 663
f. The calculation of integrals containing confluent hypergeometric functions 666
Index 671