# Mathematical Foundations of Quantum Mechanics

@inproceedings{Neumann1955MathematicalFO, title={Mathematical Foundations of Quantum Mechanics}, author={John von Neumann}, year={1955} }

Mathematical 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…

## 4,283 Citations

On the Stochastic Mechanics Foundation of Quantum Mechanics

- Physics
- 2021

Among the famous formulations of quantum mechanics, the stochastic picture developed since the middle of the last century remains one of the less known ones. It is possible to describe quantum…

Seven Principles of Quantum Mechanics

- Physics
- 2002

The list of basic axioms of quantum mechanics as it was formulated by von Neumann includes only the mathematical formalism of the Hilbert space and its statistical interpretation. We point out that…

Classical Structures in Quantum Mechanics and Applications

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- 2012

The theory of Non-Relativistic Quantum Mechanics was created (or discovered) back in the 1920's mainly by Schr\"odinger and Heisenberg, but it is fair enough to say that a more modern and unified…

Classical Physics Versus Quantum Physics: an Overview

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- 2014

The origin of quantum mechanics goes back to the mid-1920s.It was formulated first as matrix mechanics by Werner Heisenberg, Max Born and Pascual Jordan; then as wave mechanics by Louis de Broglie…

Unified Dirac-Von Neumann Formulation of Quantum Mechanics. I. Mathematical Theory

- Mathematics
- 1965

In this paper the results from various areas of mathematical research which are necessary for a consistent unification of the Dirac and von Neumann formulations of quantum mechanics are collected and…

Logical reformulation of quantum mechanics. IV. Projectors in semiclassical physics

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- 1989

This is a technical paper providing the proofs of three useful theorems playing a central role in two kinds of physical applications: an explicit logical and mathematical formulation of the…

The Formulation of Wave Mechanics

- Physics, Mathematics
- 2018

We introduce the basic physical ideas of Quantum Mechanics following the line of thought of Schrodinger Wave Mechanics. Exploiting the analogy between Optics and Mechanics, we arrive at the…

The Common Logic of Quantum Universe—Part I: The Case of Non-relativistic Quantum Mechanics

- Physics, PhilosophyFoundations of Physics
- 2022

One of the most challenging and fascinating issue in mathematical and theoretical physics concerns the possibility of identifying the logic underlying the so-called quantum universe, i.e., Quantum…

Basics of Quantum Mechanics

- Physics
- 2011

Quantum mechanics was started after works by Heisenberg (Z. Phys. 43:172, 1927), Schrodinger (Naturwissenschaften 48:52, 1935) and Dirac around 1925. Together with relativity theory it is the most…