Mathematical Foundations of Quantum Mechanics: New Edition

by John von Neumann, Robert T. Beyer (Translator), Nicholas A. Wheeler (Editor)

Overview

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.

Product Details

ISBN-13:	9780691178578
Publisher:	Princeton University Press
Publication date:	02/27/2018
Series:	Princeton Landmarks in Mathematics and Physics , #58
Edition description:	New Edition
Pages:	328
Product dimensions:	7.00(w) x 9.90(h) x 0.80(d)

About the Author

John von Neumann (1903–57) was one of the most important mathematicians of the twentieth century. His work included fundamental contributions to mathematics, physics, economics, and the development of the atomic bomb and the computer. He was a founding member of the Institute for Advanced Study in Princeton. Nicholas A. Wheeler is a mathematical physicist and professor emeritus of physics at Reed College.

Table of Contents

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

Editorial Reviews

"Lovely. . . . For anyone interested in truly understanding many of the concepts and methods within quantum mechanics which we so often take for granted, this is an invaluable book."—-Jonathan Shock, Mathemafrica

"The new edition is easier [to] read and to comprehend, and the editor thinks it will inspire the work of future generations of physicists."—-K. E. Hellwig, Zentralblatt MATH

From the Publisher

The translator and publisher have performed a service in making the classic available to a wider circle of English-speaking readers. It remains indispensable to those who desire a rigorous presentation of the foundations of the subject.

Quarterly of Applied Mathematics - A. F. Stevenson

The translator and publisher have performed a service in making the classic available to a wider circle of English-speaking readers. It remains indispensable to those who desire a rigorous presentation of the foundations of the subject.

Quarterly of Applied Mathematics - A.F. Stevenson

It remains indispensable to those who desire a rigorous presentation of the foundations of the subject.

Quarterly of Applied Mathematics