Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, EpiSciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).
Skip to Main content Skip to Navigation

Quelques modèles non linéaires en mécanique quantique

Abstract : This thesis is devoted to the study of three nonlinear models from quantum mechanics. In the first part, we prove the existence of a minimizer and of approximate excited states for the multiconfiguration methods, which aim at describing electrons in molecules. These so-defined critical points can be computed numerically by a totally new algorithm. Numerical results are provided for the first excited state of two-electron systems. In the second part, we study a mountain pass lemma modelling adiabatic reactions in the Schrödinger time-independent framework. We prove the existence of a mountain pass point, assuming that the molecules at infinity are charged or polarized. Our last part is devoted to the study of the polarization of the vacuum with the Bogoliubov-Dirac-Fock model, a relativistic mean-field theory deduced from quantum electrodynamics. Our energy is bounded from below and has a minimizer which can be interpreted as the polarized vacuum.
Document type :
Complete list of metadata
Contributor : Mathieu Lewin Connect in order to contact the contributor
Submitted on : Tuesday, June 22, 2004 - 3:45:31 PM
Last modification on : Tuesday, January 18, 2022 - 3:23:36 PM
Long-term archiving on: : Monday, September 17, 2012 - 3:35:18 PM


  • HAL Id : tel-00006306, version 1



Mathieu Lewin. Quelques modèles non linéaires en mécanique quantique. Mathématiques [math]. Université Paris Dauphine - Paris IX, 2004. Français. ⟨tel-00006306⟩



Record views


Files downloads