Existence and regularity of the solution of a time dependent Hartree-Fock equation coupled with a classical nuclear dynamics

Lucie Baudouin (1)

1 LMV - Laboratoire de Mathématiques de Versailles

We study an Helium atom (composed of one nucleus and two electrons) submitted to a general time dependent electric field, modeled by the Hartree-Fock equation, whose solution is the wave function of the electrons, coupled with the classical Newtonian dynamics, for the position of the nucleus. We prove a result of existence and regularity for the Cauchy problem, where the main ingredients are a preliminary study of the regularity in a nonlinear Schrödinger equation with semi-group techniques and a Schauder fixed point theorem.

Mots clés: existence; Hartree-Fock equation; classical dynamics; regularity; existence.

Domaines: Equations aux dérivées partielles [math.AP]

Lucie Baudouin. Existence and regularity of the solution of a time dependent Hartree-Fock equation coupled with a classical nuclear dynamics. Revista Matematica Complutense, 2005, 18 (2), pp.285-314. ⟨hal-00145715⟩