https://doi.org/10.1140/epjb/e2005-00228-x
Bayesian approach to inverse quantum statistics: Reconstruction of potentials in the Feynman path integral representation of quantum theory
Institut für Theoretische Physik,
Universität Münster, Wilhelm-Klemm Strasse 9, 48149 Münster, Germany
Corresponding author: a weiguny@uni-muenster.de
Received:
24
December
2003
Revised:
12
March
2005
Published online:
8
August
2005
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.
PACS: 02.50.Tt – Inference methods / 31.15.Kb – Path-integral methods / 05.30.-d – Quantum statistical mechanics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2005