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The two limits of the Schrödinger equation in the semi-classical approximation: discerned and non-discerned particles in classical mechanics

dc.contributor.authorGondran, Alexandre
HAL ID: 8234
ORCID: 0000-0003-0116-021X
dc.contributor.authorGondran, Michel
dc.date.accessioned2011-07-22T13:20:30Z
dc.date.available2011-07-22T13:20:30Z
dc.date.issued2011
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/6773
dc.language.isoenen
dc.subjectnon-discerned particlesen
dc.subjectapproximationen
dc.subjectSchrödinger equationen
dc.subjectquantum mechanicsen
dc.subject.ddc520en
dc.titleThe two limits of the Schrödinger equation in the semi-classical approximation: discerned and non-discerned particles in classical mechanicsen
dc.typeCommunication / Conférence
dc.contributor.editoruniversityotherEcole Nationale de l'Aviation Civile (ENAC) ENAC;France
dc.description.abstractenWe study, in the semi-classical approximation, the convergence of the quantum density and the quantum action, solutions to the Madelung equations, when the Planck constant h tends to 0. We find two different solutions which depend to the initial density . In the first case where the initial quantum density is a classical density rho_0(x), the quantum density and the quantum action converge to a classical action and a classical density which satisfy the statistical Hamilton-Jacobi equations. These are the equations of a set of classical particles whose initial positions are known only by the density rho_0(x). In the second case where initial densityen
dc.identifier.citationpages14en
dc.identifier.citationpages111-115
dc.relation.ispartofseriestitleAIP Conference Proceedings
dc.relation.ispartofseriesnumber1424
dc.relation.ispartoftitleFoundations of Probability and Physics - 6
dc.relation.ispartofeditorLarsson, Jan-Ake
dc.relation.ispartofeditorKhrennikov, Andrei
dc.relation.ispartofeditorJaeger, Gregg
dc.relation.ispartofeditorHiesmayr, Beatrix
dc.relation.ispartofeditorHaven, Emmanuel
dc.relation.ispartofeditorFei, Shao-Ming
dc.relation.ispartofeditorD'Ariano, Mauro
dc.relation.ispartofdate2011
dc.relation.isversionofdoihttp://link.aip.org/link/doi/10.1063/1.3688959
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00605920/fr/en
dc.description.sponsorshipprivateouien
dc.subject.ddclabelSciences connexes (physique, astrophysique)en
dc.relation.ispartofisbn978-0-7354-1004-6
dc.relation.conftitleFoundations of Physics and Probability (FPP6)en
dc.relation.confdate2011-06
dc.relation.confcityVäxjöen
dc.relation.confcountrySuèdeen


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