Quantum mechanics of one-and two-electron atoms

Title page......Page 1
Date-line......Page 2
Dedication......Page 3
Preface......Page 4
Contents......Page 5
Introduction. Units......Page 8
1. Separation of Schrodinger\'s equation in spherical polar coordinates. Angularly dependent eigenfunctions and the angular momentum matrix......Page 10
2. Derivation of Balmer\'s formula......Page 14
3. The radial eigenfunctions of the discrete spectrum......Page 18
4. The eigenfunctions of the continuous spectrum......Page 27
5. Motion of the nucleus......Page 31
6. Separation of Schrodinger\'s equation in parabolic coordinates......Page 33
7. Methods for the continuous spectrum for a general central potential......Page 38
8. Wave functions in momentum space. Discrete spectrum......Page 42
9. Wave functions in momentum space. Continuous spectrum......Page 46
10. General properties of the Dirac theory......Page 53
11. Angular momentum......Page 57
12. Pauli theory of the spin-electron......Page 60
13. Pauli theory for a central potential......Page 64
14. The exact solution of the Dirac equation......Page 69
15. Dirac equation. Continuous spectrum......Page 77
16. The Dirac equation in momentum space......Page 84
17. The fine structure formula......Page 89
18. Radiative corrections. $S$-matrix theory......Page 95
19. Radiative corrections. Bound states......Page 100
20. Corrections for nuclear motion and structure......Page 106
21. Fine structure and the Lamb shift......Page 109
22. Hyperfine structure splitting......Page 113
23. The fine structure of positronium......Page 120
24. The Schrodinger equation for helium (symmetry)......Page 124
25. Discussion of variation and perturbation methods......Page 127
26. Level scheme of helium......Page 130
27. Survey of approximations to be used......Page 133
28. First order Heisenberg\'s method (excited states)......Page 137
29. Polarization for excited states......Page 143
30. Fock\'s method (excited $S$-states)......Page 146
31. Hartree\'s method......Page 149
32. Ritz variation method (helium ground state)......Page 152
33. Ground state of helium-like ions with arbitrary $Z$......Page 157
34. The negative hydrogen ion......Page 160
35. Variation method for excited states......Page 163
36. Miscellaneous calculations......Page 166
37. Motion of the nucleus......Page 172
38. Discussion of the Breit equation......Page 176
39. The Pauli approximation (low $Z$)......Page 184
40. Fine structure splitting of helium......Page 189
41. Relativistic corrections for the ground state......Page 195
42. Breit equation without external field......Page 198
43. Treatment for large $Z$......Page 202
44. Hyperfine structure......Page 207
45. Zeeman effect for a single-electron atom......Page 211
46. Dependence on magnetic field strength......Page 214
47. Some corrections to the Zeeman effect......Page 219
48. Extension to many-electron atoms......Page 224
49. Comparison with precision experiments......Page 228
50. The diamagnetism of helium......Page 233
51. Linear Stark effect......Page 234
52. The quadratic Stark effect......Page 238
53. Stark effect for strong fields......Page 240
54. Ionization by the electric field. Quenching of the lines in the Stark effect......Page 241
55. Stark effect of the fine structure of hydrogen......Page 244
56. The Stark effect for weak fields......Page 247
57. Dependence on field strength......Page 250
58. The dielectric constant of helium......Page 252
59. General formulas......Page 254
60. Selection rules for orbital and magnetic quantum numbers......Page 258
61. Sum rules......Page 261
62. Proof of the sum rules......Page 265
63. The transition probabilities for hydrogen in polar coordinates......Page 268
64. Intensity of fine structure lines......Page 275
65. Intensities in parabolic coordinates (Stark effect)......Page 282
66. Higher multipole radiation......Page 284
67. Lifetimes of excited states in hydrogen......Page 290
68. Alkali and X-ray spectra......Page 298
69. General survey......Page 301
70. The Born approximation......Page 305
71. The absorption coefficient without retardation......Page 309
72. Angular distribution and retardation......Page 314
73. Relativistic effects......Page 317
74. The optical region......Page 321
75. Recombination......Page 326
76. General survey......Page 329
77. Nonrelativistic Born approximation......Page 332
78. Calculations for low energies......Page 337
79. Relativistic effects......Page 342
Appendix on spherical harmonics......Page 350
Bibliography......Page 356
Addenda and errata......Page 357
Author index......Page 366
Subject index......Page 371
Index of Tables......Page 375