Abstract (eng)
The multiconfiguration methods are a natural improvement of well-known simple models for
approximating the linear N body Schrödinger equation for atomic and molecular systems with binary
- Coulomb in realistic situations- interactions, like the Hartree and the Hartree-Fock equation.
Models like MCTDHF are intensively used for numerical simulations in quantum physics/chemistry.
However, from the mathematical point of view, these equations are yet poorly understood. The
present contribution gives the first rigorous mathematical foundation of the MCTHDH(F) equations
with the singular Coulomb interaction. In particular, we formulate in a convenient way for
the mathematical analysis the associated initial value problem for which we obtain well-posedness
results depending on the regularity of the initial data, with and without an assumption on the rank
of the associated density matrix. Also, numerical simulations of a toy model are presented with
particular interest to the so called correlation which is one of the main motivations and advantage
of the multiconfiguration methods compared to Hartree-Fock models.