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Bayesian approach to inverse quantum statistics: Reconstruction of potentials in the Feynman path integral representation of quantum theory

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  • J. C. Lemm
  • J. Uhlig
  • A. Weiguny

Abstract

The Feynman path integral representation of quantum theory is used in a non–parametric Bayesian approach to determine quantum potentials from measurements on a canonical ensemble. This representation allows to study explicitly the classical and semiclassical limits and provides a unified description in terms of functional integrals: the Feynman path integral for the statistical operator and its derivative with respect to the potential, and the integration over the space of potentials for calculating the predictive density. The latter is treated in maximum a posteriori approximation, and various approximation schemes for the former are developed and discussed. A simple numerical example shows the applicability of the method. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005

Suggested Citation

  • J. C. Lemm & J. Uhlig & A. Weiguny, 2005. "Bayesian approach to inverse quantum statistics: Reconstruction of potentials in the Feynman path integral representation of quantum theory," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 46(1), pages 41-54, July.
    • Handle: RePEc:spr:eurphb:v:46:y:2005:i:1:p:41-54
    DOI: 10.1140/epjb/e2005-00228-x
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