Bayesian Inverse Quantum Theory

Abstract.

 A Bayesian approach is developed to determine quantum-mechanical potentials from empirical data. Bayesian methods, combining empirical measurements and 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 finite temperature. The computational feasibility of the approach is demonstrated by numerical case studies. Finally, it is shown how the approach can be 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 Hartree-Fock approximation.