Existence and Regularity of the Solution of a Time Dependent Hartree-Fock Equation Coupled with a Classical Nuclear Dynamics

  • Lucie Baudouin
Palabras clave: Hartree-Fock equation, classical dynamics, regularity, existence, 2000 Mathematics Subject Classification, 35Q40, 35Q55,

Resumen

We study an Helium atom (composed of one nucleus and two electrons) submitted to a general time dependent electric field, mod led 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 Schr¨odinger equation with semi-group techniques and a Schauder fixed point theorem

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Publicado
2005-09-27
Cómo citar
Baudouin L. (2005). Existence and Regularity of the Solution of a Time Dependent Hartree-Fock Equation Coupled with a Classical Nuclear Dynamics. Revista Matemática Complutense, 18(2), 285-314. https://doi.org/10.5209/rev_REMA.2005.v18.n2.16671
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