Mathematical Foundations of Quantum MechanicsMathematical Foundations of Quantum Mechanics was a revolutionary book that caused a sea change in theoretical physics. Here, John von Neumann, one of the leading mathematicians of the twentieth century, shows that great insights in quantum physics can be obtained by exploring the mathematical structure of quantum mechanics. He begins by presenting the theory of Hermitean operators and Hilbert spaces. These provide the framework for transformation theory, which von Neumann regards as the definitive form of quantum mechanics. Using this theory, he attacks with mathematical rigor some of the general problems of quantum theory, such as quantum statistical mechanics as well as measurement processes. Regarded as a tour de force at the time of publication, this book is still indispensable for those interested in the fundamental issues of quantum mechanics. |
Contents
Introductory Considerations | 3 |
2 The Original Formulation of Quantum Mechanics | 6 |
The Transformation Theory | 17 |
Hilbert Space | 28 |
Abstract Hilbert Space | 34 |
2 The Geometry of Hilbert Space | 46 |
3 Digression on the COnditions A E | 59 |
4 Closed Linear Manifolds | 73 |
2 The Statistical Interpretation | 206 |
3 Simultaneous Measurability and Measurability in General | 211 |
4 Uncertainty Relations | 230 |
5 Projections as Propositions | 247 |
6 Radiation Theory | 254 |
Deductive Development of the Theory | 295 |
2 Proof of the Statistical Formulas | 313 |
3 Conclusions From Experiments | 328 |
5 Operators in Hilbert Space | 87 |
6 The Eigenvalue Problem | 102 |
7 Continuation | 107 |
8 Initial Considerations Concerning the Eigenvalue Problem | 119 |
9 Digression of the Existence and Uniqueness of the Solutions of the Eigenvalue Problem | 145 |
10 Commutative Operators | 170 |
11 The Trace | 178 |
The Quantum Statistics | 196 |
General Considerations | 347 |
2 Thermodynamical Considerations | 358 |
3 Reversibility and Equilibrium Problems | 379 |
4 The Macroscopic Measurement | 398 |
The Measuring Process | 417 |
2 Composite Systems | 422 |
3 Discussion of the Measuring Process | 437 |