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Probability Concepts in Quantum Mechanics

Published online by Cambridge University Press:  14 March 2022

Patrick Suppes
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Abstract

The fundamental problem considered is that of the existence of a joint probability distribution for momentum and position at a given instant. The philosophical interest of this problem is that for the potential energy functions (or Hamiltonians) corresponding to many simple experimental situations, the joint “distribution” derived by the methods of Wigner and Moyal is not a genuine probability distribution at all. The implications of these results for the interpretation of the Heisenberg uncertainty principle are analyzed. The final section consists of some observations concerning the axiomatic foundations of quantum mechanics.

Type
Research Article
Information
Philosophy of Science , Volume 28 , Issue 4 , October 1961 , pp. 378 - 389
Copyright
Copyright © Philosophy of Science Association 1961

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Footnotes

∗∗

This paper was presented on September 11, 1959 at an International Colloquium on the Axiomatic Method in Classical and Modern Mechanics, Henri Poincaré Institute, Paris.

References

Baker, G. A., Physical Review, 109 (1958), 2198.CrossRefGoogle Scholar
Dirac, P. A. M., Reviews of Modern Physics, 17 (1945), 195.CrossRefGoogle Scholar
Feynman, R. P., Reviews of Modern Physics, 20 (1948), 367.CrossRefGoogle Scholar
Koopman, B. O., Proc. of Symposia in Applied Math., vol. VII, Applied Probability, New York, 1947, pp. 97-102.Google Scholar
Mackey, G. W., Amer. Mathematical Monthly, 64 (1957), 45.CrossRefGoogle Scholar
Moyal, J. E., Proc. Cambridge Phil. Soc., 45 (1949), 99.CrossRefGoogle Scholar
Reichenbach, H., Philosophic Foundations of Quantum Mechanics, Los Angeles, 1944.Google Scholar
Rubin, H., The Axiomatic Method With Special Reference to Geometry and Physics, edited by L. Henkin, P. Suppes and A. Tarski, Amsterdam, 1959, pp. 333–340.Google Scholar
Weyl, H., The Theory of Groups and Quantum Mechanics, trans. by H. P. Robertson, New York, 1931.Google Scholar
Wigner, E., Physical Review, 40 (1932), 749.CrossRefGoogle Scholar