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J. C Lemm, J. Uhlig, and A. Weiguny (2000)

A Bayesian Approach to Inverse Quantum Statistics

Phys. Rev. Lett., 84:2068–2071.

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 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. The number of measurements being small compared to the degrees of freedom of a nonparametric estimate, the results depend strongly on the implemented a priori information.

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