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hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorLewin, Mathieu
HAL ID: 1466
ORCID: 0000-0002-1755-0207
dc.date.accessioned2018-01-15T14:17:56Z
dc.date.available2018-01-15T14:17:56Z
dc.date.issued2017
dc.identifier.issn0377-9017
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17336
dc.language.isoenen
dc.subjectHartree-Fock theoryen
dc.subjectExcited statesen
dc.subjectPalais-Smale propertyen
dc.subjectMin-max methodsen
dc.subjectAtoms and moleculesen
dc.subjectHVZ theoremen
dc.subject.ddc520en
dc.titleExistence of Hartree-Fock excited states for atoms and moleculesen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenFor neutral and positively charged atoms and molecules, we prove the existence of infinitely many Hartree-Fock critical points below the first energy threshold (that is, the lowest energy of the same system with one electron removed). This is the equivalent, in Hartree-Fock theory, of the famous Zhislin-Sigalov theorem which states the existence of infinitely many eigenvalues below the bottom of the essential spectrum of the N-particle linear Schrödinger operator. Our result improves a theorem of Lions in 1987 who already constructed infinitely many Hartree-Fock critical points, but with much higher energy. Our main contribution is the proof that the Hartree-Fock functional satisfies the Palais-Smale property below the first energy threshold. We then use minimax methods in the N-particle space, instead of working in the one-particle space.en
dc.relation.isversionofjnlnameLetters in Mathematical Physics
dc.relation.isversionofjnlvolonline firsten
dc.relation.isversionofjnldate2017
dc.relation.isversionofjnlpages22en
dc.relation.isversionofdoi10.1007/s11005-017-1019-yen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01570624en
dc.relation.isversionofjnlpublisherD. Reidelen
dc.subject.ddclabelSciences connexes (physique, astrophysique)en
dc.relation.forthcomingouien
dc.relation.forthcomingprintouien
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2018-01-15T14:11:10Z
hal.author.functionaut


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