A new method is presented to reconstruct the potential of a quantum mechani
cal many-body system from observational data, combining a nonparametric Bay
esian approach with a Hartree-Fock approximation. A priori information is i
mplemented as a stochastic process, defined on the space of potentials. The
method is computationally feasible and provides a general framework to tre
at inverse problems for quantum mechanical many-body systems.