Solutions of the multiconfiguration time-dependent Hartree-Fock equations with Coulomb interactions

Multiconfiguration methods are a natural generalization of well-known simple models for approximating the linear N body Schrödinger equation for atomic and molecular systems with binary (Coulomb) interactions, like the Hartree and the Hartree-Fock theories. This Note discusses the case of the multiconfiguration time-dependent Hartree-Fock (MCTDHF in short) method which consists in approximating the high-dimensional wavefunction by a time-dependent linear combination of Slater determinants. We formulate the system of equations of motion and we establish the well-posedness of this system in a convenient Hilbert space framework, at least as long as the associated one-particle density matrix keeps the same rank. Our proof covers and simplifies previous well-posedness results of the Cauchy problems associated to the time-dependent Hartree and the time-dependent Hartree-Fock approximations obtained elsewhere. To cite this article: S. Trabelsi, C. R. Acad. Sci. Paris, Ser. I 345 (2007).