A Bayesian Approach to Inverse Quantum Statistics

Preprint

1 July 1999

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.cond-mat/9907013

Abstract

A nonparametric Bayesian approach is developed to determine quantum potentials from empirical data for quantum systems at finite temperature. The approach combines the likelihood model of quantum mechanics with a priori information over potentials implemented in form of stochastic processes. Its specific advantages are the possibilities to deal with heterogeneous data and to express a priori information explicitly, i.e., directly in terms of the potential of interest. A numerical solution in maximum a posteriori approximation was feasible for one--dimensional problems. Using correct a priori information turned out to be essential.

Keywords

NONPARAMETRIC BAYESIAN
STOCHASTIC PROCESSES
QUANTUM STATISTICS
QUANTUM POTENTIALS
PRIORI INFORMATION
NUMERICAL SOLUTION
BAYESIAN APPROACH
INVERSE QUANTUM
TEMPERATURE

All Related Versions

Version 1, 1999-07-01, ArXiv
Published version: Physical Review Letters, 84 (10), 2068.

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