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On the Schrödinger Equation for Time-Dependent Hamiltonians with a Constant Form Domain

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Análisis Aplicadoes
dc.contributor.authorBalmaseda Martín, Ángel Aitor
dc.contributor.authorLonigro, Davide
dc.contributor.authorPérez Pardo, Juan Manuel
dc.contributor.funderComunidad de Madrides
dc.contributor.funderMinisterio de Ciencia, Innovación y Universidades (España)es
dc.contributor.funderUniversidad Carlos III de Madrides
dc.date.accessioned2022-06-23T08:31:16Z
dc.date.available2022-06-23T08:31:16Z
dc.date.issued2022-01-11
dc.description.abstractWe study two seminal approaches, developed by B. Simon and J. Kisynski, to the wellposedness of the Schrödinger equation with a time-dependent Hamiltonian. In both cases, the Hamiltonian is assumed to be semibounded from below and to have a constant form domain, but a possibly non-constant operator domain. The problem is addressed in the abstract setting, without assuming any specific functional expression for the Hamiltonian. The connection between the two approaches is the relation between sesquilinear forms and the bounded linear operators representing them. We provide a characterisation of the continuity and differentiability properties of form-valued and operator-valued functions, which enables an extensive comparison between the two approaches and their technical assumptions.en
dc.description.sponsorshipA.B. and J.M.P.-P. acknowledge support provided by the “Ministerio de Ciencia e Innovación” Research Project PID2020-117477GB-I00, by the QUITEMAD Project P2018/TCS-4342 funded by Madrid Government (Comunidad de Madrid-Spain) and by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of “Research Funds for Beatriz Galindo Fellowships” (C&QIG-BG-CM-UC3M), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation). A.B. acknowledges financial support by “Universidad Carlos III de Madrid” through Ph.D. Program Grant PIPF UC3M 01-1819 and through its mobility grant in 2020. D.L. was partially supported by “Istituto Nazionale di Fisica Nucleare” (INFN) through the project “QUANTUM” and the Italian National Group of Mathematical Physics (GNFM-INdAM).en
dc.format.extent20
dc.identifier.bibliographicCitationBalmaseda, A., Lonigro, D., & Pérez-Pardo, J. M. (2022). On the Schrödinger Equation for Time-Dependent Hamiltonians with a Constant Form Domain. In Mathematics, 10(2), 218-238en
dc.identifier.doihttps://doi.org/10.3390/math10020218
dc.identifier.issn2227-7390
dc.identifier.publicationfirstpage218
dc.identifier.publicationissue2
dc.identifier.publicationlastpage238
dc.identifier.publicationtitleMathematicsen
dc.identifier.publicationvolume10
dc.identifier.urihttps://hdl.handle.net/10016/35247
dc.identifier.uxxiAR/0000030936
dc.language.isoengen
dc.publisherMDPI AGen
dc.relation.projectIDGobierno de España. PID2020-117477GB-I00es
dc.relation.projectIDComunidad de Madrid. P2018/TCS-4342es
dc.relation.projectIDUniversidad Carlos III de Madrid. C&QIG-BG-CM-UC3Mes
dc.relation.projectIDUniversidad Carlos III de Madrid. UC3M 01-1819es
dc.rights© 2022 by the authors. Licensee MDPI, Basel, Switzerland.en
dc.rightsAtribución 3.0 España*
dc.rights.accessRightsopen accessen
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/es/*
dc.subject.ecienciaMatemáticases
dc.subject.otherSchrödinger equationen
dc.subject.otherTime-dependent hamiltonianen
dc.subject.otherHilbert scalesen
dc.subject.otherTime-dependent domainen
dc.titleOn the Schrödinger Equation for Time-Dependent Hamiltonians with a Constant Form Domainen
dc.typeresearch article*
dc.type.hasVersionVoR*
dspace.entity.typePublication
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