Mathematical Foundations of Quantum Mechanics

by Mackey, George W.

• ISBN13: 9780486435176
• ISBN10: 0486435172
• Format: Paperback
• Copyright: 2004-01-23
• Publisher: Dover Publications

Summary

Designed for students familiar with abstract mathematics but not physics, this graduate-level text was written by a member of the National Academy of Science. It introduces fundamentals of classical mechanics; surveys basics of quantum mechanics; and concludes with a look at group theory and quantum mechanics of the atom. 1963 edition.

Table of Contents

Editor's Foreword	v
Preface	vii
Chapter 1. CLASSICAL MECHANICS	1	(55)
1-1 Preliminaries	1	(2)
1-2 The Laws of Particle Mechanics	3	(7)
1-3 Generalized Coordinates and Differentiable Manifolds	10	(19)
1-4 Oscillations, Waves, and Hilbert Space	29	(18)
1-5 Statistical Mechanics	47	(9)
Chapter 2. QUANTUM MECHANICS	56	(59)
2-1 The Old Quantum Theory	56	(5)
2-2 The Quantum-Mechanical Substitute for Phase Space	61	(20)
2-3 Quantum Dynamics and the Schrödinger Equation	81	(4)
2-4 The Canonical "Quantization" of a Classical System	85	(11)
2-5 Some Elementary Examples and the Original Discoveries of Schrödinger and Heisenberg	96	(4)
2-6 Generalized Coordinates	100	(4)
2-7 Linear Systems and the Quantization of the Electromagnetic Field	104	(8)
2-8 Quantum-Statistical Mechanics	112	(3)
Chapter 3. GROUP THEORY AND THE QUANTUM MECHANICS OF THE ATOM	115	(20)
3-1 Preliminaries	115	(1)
3-2 Basic Notions in the Theory of Group Representations	115	(5)
3-3 Perturbations and the Group Theoretical Classification of Eigenvalues	120	(3)
3-4 Spherical Symmetry and Spin	123	(7)
3-5 The n-Electron Atom and the Pauli Exclusion Principle	130	(5)
Appendix	135