Mathematical Foundations of Quantum Mechanics

Translator's Preface vii
Preface to This New Edition ix
Foreword xi
Introduction 1
I Introductory Considerations
1 The Origin of the Transformation Theory 5
2 The Original Formulations of Quantum Mechanics 7
3 The Equivalence of the Two Theories: The Transformation Theory 13
4 The Equivalence of the Two Theories: Hilbert Space 21
II Abstract Hilbert Space
1 The Definition of Hilbert Space 25
2 The Geometry of Hilbert Space 32
3 Digression on the Conditions A-E 40
4 Closed Linear Manifolds 48
5 Operators in Hilbert Space 57
6 The Eigenvalue Problem 66
7 Continuation 69
8 Initial Considerations Concerning the Eigenvalue Problem 77
9 Digression on the Existence and Uniqueness of the Solutions of the Eigenvalue Problem 93
10 Commutative Operators 109
11 The Trace 114
III The Quantum Statistics
1 The Statistical Assertions of Quantum Mechanics 127
2 The Statistical Interpretation 134
3 Simultaneous Measurability and Measurability in General 136
4 Uncertainty Relations 148
5 Projections as Propositions 159
6 Radiation Theory 164
IV Deductive Development of the Theory
1 The Fundamental Basis of the Statistical Theory 193
2 Proof of the Statistical Formulas 205
3 Conclusions from Experiments 214
V General Considerations
1 Measurement and Reversibility 227
2 Thermodynamic Considerations 234
3 Reversibility and Equilibrium Problems 247
4 The Macroscopic Measurement 259
VI The Measuring Process
1 Formulation of the Problem 271
2 Composite Systems 274
3 Discussion of the Measuring Process 283
Name Index 289
Subject Index 291
Locations of Flagged Propositions 297
Articles Cited: Details 299
Locations of the Footnotes 303