Group theory and quantum mechanics

B. L. van der Waerden038706740X, 9780387067407, 354006740X, 9783540067405

Table of contents :
Table of Contents……Page 5
Preface……Page 4
1. Wave Functions……Page 7
2. Hilbert Spaces……Page 10
3. Linear Operators……Page 15
4. Hypermaximal Operators……Page 18
5. Separation of Variables……Page 22
6. One Electron in a Central Field……Page 25
7. Perturbation Theory……Page 31
8. Angular Momentum and Infinitesimal Rotations……Page 33
9. Linear Transformations……Page 38
10. Groups……Page 46
11. Equivalence and Reducibility of Representations……Page 52
12. Representations of Abelian Groups. Examples……Page 59
13. Uniqueness Theorems……Page 65
14. Kronecker’s Product Transformation……Page 67
15. The Operators Commuting with all Operators of a Given Representation……Page 72
16. Representations of Finite Groups……Page 77
17. Group Characters……Page 84
A. Lie Groups……Page 88
B. One-dimensional Lie Groups and Semi-Groups……Page 89
C. Causality and Translations in Time……Page 92
D. The Lie Algebra of a Lie Group……Page 93
E. Representations of Lie Groups……Page 95
19. The Unitary Groups SU(2) and the Rotation Group O_3……Page 96
20. Representations of the Rotation Group O_3……Page 102
A. The Product Representation rho_j times rho_{j’}……Page 107
B. The Clebsch-Gordan Series……Page 108
C. Applications of (21.1)……Page 113
D. The Reflection Character……Page 115
22. Selection and Intensity Rules……Page 116
A. The Group SL(2) and the Restricted Lorentz Group……Page 120
B. Infinitesimal Transformations……Page 123
C. The Relation between World Vectors and Spinors……Page 126
24. The Spin……Page 129
A. Pauli’s Pair of Functions (psi_1, psi_2)……Page 131
B. Transformation of the Pair (psi_1, psi_2)……Page 132
C. Infinitesimal Rotations……Page 134
D. The Angular Momenta……Page 135
E. The Doublet Splitting of the Alkali Terms……Page 137
26. Dirac’s Wave Equation……Page 138
A. Dirac’s Equation Rewritten……Page 143
B. Weyl’s Equation……Page 146
28. The Several Electron Problem. Multiplet Structure. Zeeman Effect……Page 147
29. The Resonance of Equal Particles……Page 154
30. The Exclusion Principle and the Periodical System……Page 163
31. The Eigenfunctions of the Atom……Page 167
32. The Calculation of the Energy Values……Page 177
33. Pure Spin Functions and their Transformation under Rotations and Permutations……Page 180
34. Representations of the Symmetric Group S_n……Page 188
35. The Quantum Numbers of the Molecule……Page 194
36. The Rotation Levels……Page 201
37. The Case of Two Equal Nuclei……Page 208
Index……Page 210