This is a report on a joint work with Isabelle Catto, Norbert Mauser and Saber Trabelsi. The Multiconfiguration time dependent Hartree Fock Method (MCTDHF) is a nonlinear approximation of a linear system of /N/ quantum particles with binary interaction. It combines the principle of the Hartree Fock and the Galerkin approximation. The main difficulty is the introduction of a global (in space) density matrix $\Gamma(t) $ which may degenerate. By construction this approximation formally preserves the mass and the energy of the system. The conservation of energy can be used to balance the singularities Coulomb potential and to provide sufficient conditions for the global in time invertibility of $\Gamma(t)$.

In numerical computations this matrix is very often regularized (changed into $\Gamma(t) +\epsilon(t)$). In this situation the energy is no more conserved
and the mathematical analysis done in $L^2$ relies on Strichartz type estimates.