The Mathematical Foundations of Quantum Mechanics: a Lecture-Note Volume

Cover......Page 1
Editor's Foreword......Page 5
Preface......Page 7
Contents......Page 9
1.1 Preliminaries......Page 13
1.2 The Laws of Particle Mechanics......Page 15
1.3 Generalized Coordinates and Differentiable Manifolds......Page 22
1.4 Oscillations, Waves, and Hilbert Space......Page 41
1.5 Statistical Mechanics......Page 59
2.1 The Old Quantum Theory......Page 68
2.2 The Quantum-Mechanical Substitute for Phase Space......Page 73
2.3 Quantum Dynamics and the Schrodinger Equation......Page 93
2.4 The Canonical "Quantization" of a Classical System......Page 97
2.5 Some Elementary Examples and the Original Discoveries of Schrodinger and Heisenberg......Page 108
2.6 Generalized Coordinates......Page 112
2.7 Linear Systems and the Quantization of the Electromagnetic Field......Page 116
2.8 Quantum-Statistical Mechanics......Page 124
3.2 Basic Notions in the Theory of Group Representations......Page 127
3.3 Perturbations and the Group Theoretical Classification of Eigenvalues......Page 132
3.4 Spherical Symmetry and Spin......Page 135
3.5 The n-Electron Atom and the Pauli Exclusion Principle......Page 142
Appendix......Page 147