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