The theory of groups and quantum mechanics

Cover......Page 1
Title Page......Page 4
Copyright Page......Page 5
Dedication......Page 6
Author\'s Preface to the First German Edition......Page 8
Author\'s Preface to the Second German Edition......Page 10
Translator\'s Preface......Page 14
Contents......Page 16
Introduction......Page 20
1. The n-dimensional Vector Space.......Page 26
2. Linear Correspondences. Matrix Calculus......Page 30
3. The Dual Vector Space......Page 37
4. Unitary Geometry and Hermitian Forms......Page 40
5. Transformation to Principal Axes......Page 46
6. Infinitesimal Unitary Transformations......Page 52
7. Remarks on oo-dimensional Space......Page 56
1. Physical Foundations......Page 66
2. The de Broglie Waves of a Particle......Page 73
3. Schrddinger\'s Wave Equation. The Harmonic Oscillator......Page 79
4. Spherical Harmonics......Page 85
5. Electron in Spherically Symmetric Field. Directional Quantization......Page 88
6. Collision Phenomena......Page 95
7. The Conceptual Structure of Quantum Mechanics......Page 99
8. The Dynamical Law. Transition Probabilities......Page 105
9. Perturbation Theory......Page 111
10. The Problem of Several Bodies. Product Space......Page 114
11. Commutation Rules. Canonical Transformations......Page 118
12. Motion of a Particle in an Electro-magnetic Field. Zeeman Effect and Stark Effect......Page 123
13. Atom in Interaction with Radiation......Page 127
III. GROUPS AND THEIR REPRESENTATIONS......Page 135
1. Transformation Groups......Page 
2. Abstract Groups and their Realization......Page 138
3. Sub-groups and Conjugate Classes......Page 141
4. Representation of Groups by Linear Transformations......Page 145
5. Formal Processes. Clebsch-Gordan Series......Page 148
6. The Jordan-Hdlder Theorem and its Analogues......Page 156
7. Unitary Representations......Page 161
8. Rotation and Lorentz Groups......Page 165
9  Character of a Representation......Page 175
10. Schur\'s Lemma and Burnside\'s Theorem......Page 177
11. Orthogonality Properties of Group Characters......Page 182
12. Extension to Closed Continuous Groups......Page 185
13. The Algebra of a Group......Page 190
14. Invariants and Covanants......Page 195
15. Remarks on Lie\'s Theory of Continuous Groups of Transformations......Page 200
16. Representation by Rotations of Ray Space......Page 205
1. The Representation Induced in System Space by the Rotation Group......Page 210
2. Simple States and Term Analysis. Examples......Page 216
3. Selection and Intensity Rules......Page 222
4. The Spinning Electron, Multiplet Structure and Anomalous Zeeman Effect......Page 227
5. Relativistically Invariant Equations of Motion of an Electron......Page 235
6  Energy and Momentum. Remarks on the Interchange of Past and Future......Page 243
7. Electron in Spherically Symmetric Field......Page 252
8. Selection Rules. Fine Structure......Page 257
9. Resonance between Equivalent Individuals......Page 263
10. The Pauli Exclusion Principle and the Structure of the Periodic Table......Page 267
11  The Problem of. Several Bodies and the Quantization of the Wave Equation......Page 271
12. Quantization of the Maxwell-Dirac Field Equations......Page 278
13. The Energy and Momentum Laws of Quantum Physics. Relativistic Invariance......Page 289
14. Quantum Kinematics as an Abelian Group of Rotations......Page 297
15. Derivation of the Wave Equation from the Commutation Rules......Page 302
1. The Group induced in Tensor Space and the Algebra of  Symmetric Transformations......Page 306
2. Symmetry Classes of Tensors......Page 311
3. Invariant Sub-spaces in Group Space......Page 316
4. Invariant Sub-spaces in Tensor Space......Page 321
5. Fields and Algebras......Page 327
6. Representations of Algebras......Page 329
7. Constructive Reduction of an Algebra into Simple Matric Algebras......Page 334
8. The Characters of the Symmetric Group and Equivalence Degeneracy in Quantum Mechanics......Page 344
9. Relation between the Characters of the Symmetric Permutation and Affine Groups......Page 351
10. Direct Product. Sub-groups......Page 357
11. Perturbation Theory for the Constructiop of Molecules......Page 364
12. The Syi*rnetry Problem of Quantum Theory......Page 372
13. Young\'s Symmetry Operators......Page 383
14. Irreducibility, Linear Independence, Inequivalence and Completeness......Page 387
15. Spin and Valence. Group-theoretic Classification of Atomic Spectra......Page 394
16. Determination of the Primitive Characters of u and it......Page 402
17. Calculation of Volume on u......Page 411
18. Branching Laws......Page 415
1. PROOF OF AN INEQUALITY......Page 418
2. A COMPOSITION PROPERTY OF GROUP CHARACTERS......Page 420
3. A THEOREM CONCERNING NON-DEGENERATE ANTI-SYMMETRIC BI-LINEAR FORMS......Page 422
BIBLIOGRAPHY......Page 424
LIST OF OPERATIONAL SYMBOLS......Page 434
LIST OF LETTERS HAVING A FIXED SIGNIFICANCE......Page 435
INDEX......Page 438