A bilinear optimal control problem applied to a time dependent Hartree-Fock equation coupled with classical nuclear dynamics
type: Item
instance of: scholarly article
title: A bilinear optimal control problem applied to a time dependent Hartree-Fock equation coupled with classical nuclear dynamics
zbMATH Open document ID: 1109.49003
author: Lucie Baudouin
published in: Portugaliae Mathematica. Nova Série
publication date: 2006-12-11T00:00:00Z
full work available at URL: https://eudml.org/doc/53082
review text: Summary: We study a problem of bilinear optimal control for the electronic wave function of an Helium atom by an external time dependent electric field. The behavior of the atom is modeled by the Hartree-Fock equation, whose solution is the wave function of the electrons, coupled with the classical Newtonian dynamics, corresponding to the motion of the nucleus. We prove the existence of a bilinear optimal control in the case when the position of the nucleus is known and also prove the corresponding optimality condition. Then, we detail the proof of the existence of an optimal control for the coupled system and complete the study giving a formal optimality condition to define the electric control.
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 49K20
zbMATH DE Number: 5079775
zbMATH Keywords: optimality condition
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5079775