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

Revista Matemática Complutense (2005)

- Volume: 18, Issue: 2, page 285-314
- ISSN: 1139-1138

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topBaudouin, Lucie. "Existence and regularity of the solution of a time dependent Hartree-Fock equation coupled with a classical nuclear dynamics.." Revista Matemática Complutense 18.2 (2005): 285-314. <http://eudml.org/doc/38167>.

@article{Baudouin2005,

abstract = {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.},

author = {Baudouin, Lucie},

journal = {Revista Matemática Complutense},

keywords = {Ecuación de Hartree-Fock; Función de onda; Dinámica nuclear; Ecuación de Schrödinger; Unicidad; Dinámica clásica; Hartree-Fock equation; classical nuclear dynamics; Cauchy problem},

language = {eng},

number = {2},

pages = {285-314},

title = {Existence and regularity of the solution of a time dependent Hartree-Fock equation coupled with a classical nuclear dynamics.},

url = {http://eudml.org/doc/38167},

volume = {18},

year = {2005},

}

TY - JOUR

AU - Baudouin, Lucie

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

JO - Revista Matemática Complutense

PY - 2005

VL - 18

IS - 2

SP - 285

EP - 314

AB - 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.

LA - eng

KW - Ecuación de Hartree-Fock; Función de onda; Dinámica nuclear; Ecuación de Schrödinger; Unicidad; Dinámica clásica; Hartree-Fock equation; classical nuclear dynamics; Cauchy problem

UR - http://eudml.org/doc/38167

ER -

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