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The quantum probability calculus

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References

  • Belinfante, F. J., A Survey of Hidden Variable Theories, Pergamon Press, New York, 1973.

    Google Scholar 

  • Brittin, W. E. and Chappell, W. R., ‘The Wigner Distribution Function and Second Quantization in Phase Space’, Review of Modern Physics 34 (1962), 620–627.

    Google Scholar 

  • Gleason, A. M., ‘Measures on the Closed Subspaces of a Hilbert Space’, Journal of Mathematics and Mechanics 6 (1957), 885–893.

    Google Scholar 

  • Gudder, S. P., ‘Hilbert Space, Independence, and Generalized Probability’, Journal of Mathematical Analysis and Applications 20 (1967), 48–61.

    Google Scholar 

  • Gudder, S. P., ‘Joint Distributions of Observables’, Journal of Mathematics and Mechanics 18 (1968), 325–335.

    Google Scholar 

  • Gudder, S. P. and Marchand, J. P., ‘Non-Commutative Probability on von Neumann Algebras’, Journal of Mathematical Physics 13 (1972), 799–806.

    Google Scholar 

  • Gudder, S. P. and Piron, C., ‘Observables and the Field in Quantum Mechanics’, Journal of Mathematical Physics 12 (1971), 1583–1588.

    Google Scholar 

  • Jauch, J. M., Foundations of Quantum Mechanics, Addison-Wesley, Reading, 1968.

    Google Scholar 

  • Kolmogorov, A. N., Foundations of the Theory of Probability, Chelsea, New York, 1956, transl. and ed. by N. Morrison.

    Google Scholar 

  • Moyal, J. E., ‘Quantum Mechanics as a Statistical Theory’, Proceedings of the Cambridge Philosophical Society 45 (1949), 99–124.

    Google Scholar 

  • Park, J. L. and Margenau, H., ‘Simultaneous Measurability in Quantum Theory’, International Journal of Theoretical Physics 1 (1968), 211–282.

    Google Scholar 

  • Piron, C., ‘Axiomatique Quantique’, Helvetica Physica Acta 37 (1964), 439–467.

    Google Scholar 

  • Renyi, A., Probability Theory, North Holland, Amsterdam, 1970.

    Google Scholar 

  • Suppes, P., ‘Probability Concepts in Quantum Mechanics’, Philosophy of Science 28 (1961), 378–389.

    Google Scholar 

  • Suppes, P., ‘The Role of Probability in Quantum Mechanics’ in B. Baumrin (ed.), Philosophy of Science, The Delaware Seminar, Wiley, New York, 1963.

    Google Scholar 

  • Suppes, P., ‘The Probabilistic Argument for a Non-classical Logic of Quantum Mechanics’, Philosophy of Science 33 (1966), 14–21.

    Google Scholar 

  • Varadarajan, V. S., ‘Probability in Physics and a Theorem on Simultaneous Observability’, Comments on Pure and Applied Mathematics 15 (1962), 189–216.

    Google Scholar 

  • Wigner, E., ‘On the Quantum Theory for Thermodynamic Equilibrium’, Physical Review 40 (1932), 749–759.

    Google Scholar 

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This article was written during a visit to the University of Colorado in Boulder. It is a pleasure to thank Professor K. Gustafson, who made this visit possible. Thanks are also due to Professor B. Misra for an important remark concerning the joint distribution of noncompatible observables.

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Jauch, J.M. The quantum probability calculus. Synthese 29, 131–154 (1974). https://doi.org/10.1007/BF00484955

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