Bayesian Inverse Quantum Theory
Jörg C. Lemm, Joerg Uhlig
Institut für Theoretische Physik I,
D-48149 Münster, Germany
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.