Quantum mechanics was still in its infancy in 1932 when the young John von Neumann, who would go on to become one of the greatest mathematicians of the twentieth century, published Mathematical Foundations of Quantum Mechanics--a revolutionary book that for the first time provided a rigorous mathematical framework for the new science. Robert Beyer's 1955 English translation, which von Neumann reviewed and approved, is cited more frequently today than ever before. But its many treasures and insights were too often obscured by the limitations of the way the text and equations were set on the page. In this new edition of this classic work, mathematical physicist Nicholas Wheeler has completely reset the book in TeX, making the text and equations far easier to read. He has also corrected a handful of typographic errors, revised some sentences for clarity and readability, provided an index for the first time, and added prefatory remarks drawn from the writings of Léon Van Hove and Freeman Dyson. The result brings new life to an essential work in theoretical physics and mathematics.

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