Bayesian approach to inverse quantum statistics
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 on potentials implemented in the form of stochastic processes. Its specific advantages are the possibilities to deal with heterogeneous data and to express a priori information explicitly in terms of the potential of interest. A numerical solution in maximum a posteriori approximation is obtained for one-dimensional problems. As nonparametric estimates, the results depend strongly on the implemented a priori information.
Lemm
JC
Institut fur Theoretische Physik I, Universitat Munster, 48149 Munster, Germany.
Uhlig
J
Weiguny
A