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The multiconfiguration methods are widely used by quantum physicists andchemists for numerical approximation of the many electron Schr\"odingerequation. Recently, first mathematically rigorous results were obtained on thetime-dependent models, e.g. short-in-time well-posedness in the Sobolev space$H^2$ for bounded interactions (C. Lubichand O. Koch} with initial data in$H^2$, in the energy space for Coulomb interactions with initial data in thesame space (Trabelsi, Bardos et al.}, as well as global well-posedness under asufficient condition on the energy of the initial data (Bardos et al.). Thepresent contribution extends the analysis by setting an $L^2$ theory for theMCTDHF for general interactions including the Coulomb case. This kind ofresults is also the theoretical foundation of ad-hoc methods used in numericalcalculation when modification ("regularization") of the density matrix destroysthe conservation of energy property, but keeps invariant the mass.

$L^2$ Analysis of the Multi-Configuration Time-Dependent Hartree-Fock Equations