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One particle equations for many particle quantum systems: The MCTHDF method

This contribution is devoted to the mathematical analysis of more or less sophisticated approximations of the time evolution of systems of N quantum particles. New results for the Multiconfiguration Time Dependent Hartree-Fock (MCTDHF) method (which cover the material of the talk given by the first author at the "Nonlinear waves conference in honor of Walter Strauss") are summarized and compared with the simpler Hartree and Hartree-Fock equations.