Foundations of Quantum Mechanics II (Theoretical and Mathematical Physics)

Contents......Page 8
1 Maximal Decision Observables......Page 16
2 Representation of H as L^2(Sp(A), \mu) where Sp(A) is the Spectrum of a Scale Observable A......Page 21
3 Improper Scalar and Vector Functions Defined on Sp(A)......Page 28
4 Transformation of One Representation into Another......Page 37
5 Position and Momentum Representation......Page 42
6 Degenerate Spectra......Page 51
1 The Heisenberg Picture......Page 55
2 The Schrodinger Picture......Page 63
3 The Interaction Picture......Page 68
4 Time Reversal Transformations......Page 71
XI The Spectrum of One-Electron Systems......Page 76
1 The Effect of the Emission of a Photon......Page 77
2 Ensembles Consisting of Bound States......Page 86
3 The Spectrum of Hydrogen-like Atoms......Page 87
4 The Eigenfunctions for the Discrete Spectrum......Page 93
5 The Continuous Spectrum......Page 96
6 Perturbation Theory......Page 99
7 Perturbation Computations and Symmetry......Page 102
8 The Spectrum of Alkali Atoms......Page 105
9 Electron Spin......Page 107
10 Addition of Angular Momentum......Page 108
11 Fine Structure of Hydrogen and Alkali Metals......Page 114
1 The Hilbert Space and the Hamiltonian Operator for the Internal Motion of Atoms with n Electrons......Page 119
2 The Spectrum of Two-Electron Atoms......Page 121
3 Ritz Variational Principle......Page 124
4 The Fine Structure of the Helium Spectrum......Page 129
1 Intensity of Spectral Lines......Page 132
2 Representation Theory and Matrix Elements......Page 133
3 Selection Rules for One-Electron Spectra......Page 135
4 Selection Rules for the Helium Spectrum......Page 138
1 Energy Terms in the Absence of Spin......Page 139
2 Fine Structure Splitting of Spectral Lines......Page 143
3 Structure Principles......Page 145
4 The Periodic System of the Elements......Page 150
5 Selection and Intensity Rules......Page 158
6 Zeeman Effect......Page 162
7 f Electron Problems and the Symmetric Group......Page 166
8 The Characters for the Representations of S_f and U_n......Page 175
9 Perturbation Computations......Page 185
1 The Hamiltonian Operator for a Molecule......Page 192
2 The Form of the Eigenfunctions......Page 193
3 The Ionized Hydrogen Molecule......Page 195
4 Structure Principles for Molecular Energy Levels......Page 202
5 Formation of a Molecule from Two Atoms......Page 203
6 The Hydrogen Molecule......Page 206
7 The Chemical Bond......Page 209
8 Spectra of Diatomic Molecules......Page 223
9 The Effect of Electron Spin on Molecular Energy Levels......Page 228
1 General Properties of Ensembles Used in Scattering Experiments......Page 230
2 General Properties of Effects Used in Scattering Experiments......Page 237
3 Separation of Center of Mass Motion......Page 239
4.1 Definition of the Wave Operators......Page 241
4.2 Some General Properties of Wave Operators......Page 243
4.3 Wave Operators and the Spectral Representation of the Hamiltonian Operators......Page 248
4.4 The S Operator......Page 251
4.5 A Sufficient Condition for the Existence of Normal Wave Operators......Page 253
4.6 The Existence of Complete Wave Operators......Page 258
4.7 Stationary Scattering Theory......Page 268
4.8 Scattering of a Pair of Identical Elementary Systems......Page 271
4.9 Multiple-Channel Scattering Theory......Page 272
5.1 Scattering of an Elementary System of Spin 1/2 by an Elementary System of Spin 0......Page 274
5.2 The Born Approximation......Page 277
5.3 Scattering of an Electron by a Hydrogen Atom......Page 278
6 Examples of Registrations in Scattering Experiments......Page 283
6.1 The Effect of the "Impact" of a Microsystem on a Surface......Page 284
6.2 Counting Microsystems Scattered into a Solid Angle......Page 290
6.3 The Scattering Cross Section......Page 308
7 Survey of Other Problems in Scattering Theory......Page 312
XVII The Measurement Process and the Preparation Process......Page 318
1 The Problem of Consistency......Page 319
2.1 Measurement with a Microscope......Page 322
2.2 Measurement Scattering Morphisms......Page 326
2.3 Properties of Measurement Scattering Morphisms......Page 328
3 Measurement Transformations......Page 331
3.2 Properties of Measurement Transformation Morphisms......Page 332
4 Transpreparations......Page 334
4.1 Reduction of a Preparation Procedure by Means of a Registration Procedure......Page 336
4.2 Transpreparation by Means of Scattering......Page 338
4.3 Collapse of Wave Packets?......Page 341
4.4 The Einstein-Podolski-Rosen Paradox......Page 345
5 Measurements of the First Kind......Page 349
6 The Physical Importance of Scattering Processes Used for Registration and Preparation......Page 355
6.1 Sequences of Measurement Scatterings and Measurement Transformations......Page 356
6.2 Physical Importance of Measurement Scattering and Measurement Transformations......Page 358
6.3 Chains of Transpreparations......Page 361
6.4 The Importance of Transpreparators for the Preparation Process......Page 362
6.5 Unstable States......Page 363
7 Complex Preparation and Registration Processes......Page 369
1 Universality of Quantum Mechanics?......Page 370
2 Macroscopic Systems......Page 372
3 Compatibility of the Measurement Process with Preparation and Registration Procedures......Page 378
4 "Point in Time" of Measurement in Quantum Mechanics?......Page 380
5 Relationships Between Different Theories and Quantum Mechanics......Page 382
6 Quantum Mechanics and Cosmology......Page 386
7 Quantum Mechanics and Physical World Views......Page 388
1 Groups......Page 390
2 Cosets and Invariant Subgroups......Page 391
4 Isomorphism Theorem......Page 392
5 Direct Products......Page 393
6 Representations of Groups......Page 394
7 The Irreducible Representations of a Finite Group......Page 395
8 Orthogonality Relations for the Elements of Irreducible Representation Matrices......Page 398
9 Representations of the Symmetric Group......Page 400
10.1 The Species of Structure: Topological Group......Page 404
10.3 Lie Groups......Page 406
10.4 Representations of Topological Groups......Page 410
10.5 Group Rings of Compact Lie Groups......Page 413
10.6 Representations in Hilbert Space......Page 420
10.7 Representations up to a Factor......Page 422
References......Page 425
Index......Page 429