Probability concepts in quantum mechanics

Philosophy of Science 28 (4):378-389 (1961)
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
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DOI 10.1086/287824
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The Quantum Probability Calculus.J. M. Jauch - 1974 - Synthese 29 (1-4):131 - 154.
Partial and Unsharp Quantum Logics.M. L. Dalla Chiara & R. Giuntini - 1994 - Foundations of Physics 24 (8):1161-1177.

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