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A simplex of probability measures associated with classical states of the harmonic oscillator

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Abstract

The probability measures which determine the statistics of the number operator of a quantum harmonic oscillator in a classical state, constitute a convex set. By means of von Weizsäcker and Winkler's generalization of Choquet's theory, it is shown that this set is a simplex.

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References

  1. Davies, E. B., Quantum Theory of Open Systems, Academic Press, London, 1979.

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  2. von Weizsäcker, H. and Winkler, G., ‘Integral Representation in the Set of Solutions of a Generalized Moment Problem’, Math. Ann 246, 23–32 (1979).

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Authors and Affiliations

  1. Institut für Theoretische Physik I, Universität Münster, D-4400, Münster, West Germany

    A. Bach

  2. Abteilung Mathematik, Universität Dortmund, D-4600, Dortmund 50, West Germany

    U. Lüxmann-Ellinghaus

Authors
  1. A. Bach
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  2. U. Lüxmann-Ellinghaus
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Bach, A., Lüxmann-Ellinghaus, U. A simplex of probability measures associated with classical states of the harmonic oscillator. Lett Math Phys 9, 103–106 (1985). https://doi.org/10.1007/BF00400706

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  • DOI: https://doi.org/10.1007/BF00400706

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