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Mathematical Foundations of Quantum MechanicsNew Edition$
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John von Neumann

Print publication date: 2018

Print ISBN-13: 9780691178561

Published to Princeton Scholarship Online: September 2018

DOI: 10.23943/princeton/9780691178561.001.0001

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Introductory Considerations

Introductory Considerations

(p.5) Chapter I Introductory Considerations
Mathematical Foundations of Quantum Mechanics

John von Neumann

, Robert T. Beyer, Nicholas A. Wheeler
Princeton University Press

This chapter presents the origins of the transformation theory and related concepts. It shows how, in 1925, a procedure initiated by Werner Heisenberg was developed by himself, Max Born, Pascual Jordan, and a little later by Paul Dirac, into a new system of quantum theory—the first complete system of quantum theory which physics has possessed. A little later Erwin Schrödinger developed the “wave mechanics” from an entirely different starting point. This accomplished the same ends, and soon proved to be equivalent to the Heisenberg, Born, Jordan, and Dirac system. On the basis of the Born statistical interpretation of the quantum theoretical description of nature, it was possible for Dirac and Jordan to join the two theories into one, the “transformation theory,” in which they make possible a grasp of physical problems which is especially simple mathematically.

Keywords:   transformation theory, Hilbert space, Werner Heisenberg, Max Born, Pascual Jordan, Paul Dirac, quantum theory, Erwin Schrödinger, wave mechanics

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