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

Autores: Lucie Baudouin
Localización: Revista matemática complutense, ISSN-e 1988-2807, ISSN 1139-1138, Vol. 18, Nº 2, 2005, págs. 285-314
Idioma: inglés
DOI: 10.5209/rev_rema.2005.v18.n2.16671
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Resumen
- 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.