Bayesian inverse quantum theory

A Bayesian approach is developed to determine quantum-mechanical potentials from empirical data. Bayesian methods, combining empirical measurements an d a priori information, provide flexible tools for such empirical learning problems. The paper presents the basic theory, concentrating in particular on measurements of particle coordinates in quantum-mechanical systems at fi nite temperature. The computational feasibility of the approach is demonstr ated by numerical case studies. Finally, it is shown how the approach can b e generalized to such many-body and few-body systems for which a mean field description is appropriate. This is done by means of a Bayesian inverse Ha rtree-Fock approximation.