Mathematical Foundations of Quantum Mechanics

Translator's Preface viiPreface to This New Edition ixForeword xiIntroduction 1I Introductory Considerations1 The Origin of the Transformation Theory 52 The Original Formulations of Quantum Mechanics 73 The Equivalence of the Two Theories: The Transformation Theory 134 The Equivalence of the Two Theories: Hilbert Space 21II Abstract Hilbert Space1 The Definition of Hilbert Space 252 The Geometry of Hilbert Space 323 Digression on the Conditions A-E 404 Closed Linear Manifolds 485 Operators in Hilbert Space 576 The Eigenvalue Problem 667 Continuation 698 Initial Considerations Concerning the Eigenvalue Problem 779 Digression on the Existence and Uniqueness of the Solutions of the Eigenvalue Problem 9310 Commutative Operators 10911 The Trace 114III The Quantum Statistics1 The Statistical Assertions of Quantum Mechanics 1272 The Statistical Interpretation 1343 Simultaneous Measurability and Measurability in General 1364 Uncertainty Relations 1485 Projections as Propositions 1596 Radiation Theory 164IV Deductive Development of the Theory1 The Fundamental Basis of the Statistical Theory 1932 Proof of the Statistical Formulas 2053 Conclusions from Experiments 214V General Considerations1 Measurement and Reversibility 2272 Thermodynamic Considerations 2343 Reversibility and Equilibrium Problems 2474 The Macroscopic Measurement 259VI The Measuring Process1 Formulation of the Problem 2712 Composite Systems 2743 Discussion of the Measuring Process 283Name Index 289Subject Index 291Locations of Flagged Propositions 297Articles Cited: Details 299Locations of the Footnotes 303