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.
@article{urn:eudml:doc:38167,
title = {Existence and regularity of the solution of a time dependent Hartree-Fock equation coupled with a classical nuclear dynamics.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {18},
year = {2005},
pages = {285-314},
zbl = {1162.35450},
mrnumber = {MR2166510},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38167}
}
Baudouin, Lucie. Existence and regularity of the solution of a time dependent Hartree-Fock equation coupled with a classical nuclear dynamics.. Revista Matemática de la Universidad Complutense de Madrid, Tome 18 (2005) pp. 285-314. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38167/