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Expectation and transition probability

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Abstract

It is shown that a separating or order-determining set of states on a quantum logic need not determine the expectations of observables. A formula is derived for the transition probability between states. Using this formula, it is shown that the propositions do not determine the transition probability in a certain sense. The form of the transition probability is derived for pure states on Hilbert space, dominated normal states on a von Neumann algebra, and absolutely continuous states on a measurable space. A metric is defined in terms of the transition probability.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Denver, 80208, Denver, Colorado

    Stanley P. Gudder

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  1. Stanley P. Gudder
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Gudder, S.P. Expectation and transition probability. Int J Theor Phys 20, 383–395 (1981). https://doi.org/10.1007/BF00669530

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  • DOI: https://doi.org/10.1007/BF00669530

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