A nonparametric Bayesian approach is developed to determine quantum potenti
als from empirical data for quantum systems at finite temperature. The appr
oach combines the likelihood model of quantum mechanics with a priori infor
mation on potentials implemented in the form of stochastic processes. Its s
pecific advantages are the possibilities to deal with heterogeneous data an
d to express a priori information explicitly in terms of the potential of i
nterest. A numerical solution in maximum a posteriori approximation is obta
ined for one-dimensional problems. As nonparametric estimates, the results
depend strongly on the implemented a priori information.