Hartree-Fock approximation for inverse many-body problems

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.