Publication: On the Schrödinger Equation for Time-Dependent Hamiltonians with a Constant Form Domain
dc.affiliation.dpto | UC3M. Departamento de Matemáticas | es |
dc.affiliation.grupoinv | UC3M. Grupo de Investigación: Análisis Aplicado | es |
dc.contributor.author | Balmaseda Martín, Ángel Aitor | |
dc.contributor.author | Lonigro, Davide | |
dc.contributor.author | Pérez Pardo, Juan Manuel | |
dc.contributor.funder | Comunidad de Madrid | es |
dc.contributor.funder | Ministerio de Ciencia, Innovación y Universidades (España) | es |
dc.contributor.funder | Universidad Carlos III de Madrid | es |
dc.date.accessioned | 2022-06-23T08:31:16Z | |
dc.date.available | 2022-06-23T08:31:16Z | |
dc.date.issued | 2022-01-11 | |
dc.description.abstract | We 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.sponsorship | A.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.extent | 20 | |
dc.identifier.bibliographicCitation | Balmaseda, 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), 218-238 | en |
dc.identifier.doi | https://doi.org/10.3390/math10020218 | |
dc.identifier.issn | 2227-7390 | |
dc.identifier.publicationfirstpage | 218 | |
dc.identifier.publicationissue | 2 | |
dc.identifier.publicationlastpage | 238 | |
dc.identifier.publicationtitle | Mathematics | en |
dc.identifier.publicationvolume | 10 | |
dc.identifier.uri | https://hdl.handle.net/10016/35247 | |
dc.identifier.uxxi | AR/0000030936 | |
dc.language.iso | eng | en |
dc.publisher | MDPI AG | en |
dc.relation.projectID | Gobierno de España. PID2020-117477GB-I00 | es |
dc.relation.projectID | Comunidad de Madrid. P2018/TCS-4342 | es |
dc.relation.projectID | Universidad Carlos III de Madrid. C&QIG-BG-CM-UC3M | es |
dc.relation.projectID | Universidad Carlos III de Madrid. UC3M 01-1819 | es |
dc.rights | © 2022 by the authors. Licensee MDPI, Basel, Switzerland. | en |
dc.rights | Atribución 3.0 España | * |
dc.rights.accessRights | open access | en |
dc.rights.uri | http://creativecommons.org/licenses/by/3.0/es/ | * |
dc.subject.eciencia | Matemáticas | es |
dc.subject.other | Schrödinger equation | en |
dc.subject.other | Time-dependent hamiltonian | en |
dc.subject.other | Hilbert scales | en |
dc.subject.other | Time-dependent domain | en |
dc.title | On the Schrödinger Equation for Time-Dependent Hamiltonians with a Constant Form Domain | en |
dc.type | research article | * |
dc.type.hasVersion | VoR | * |
dspace.entity.type | Publication |
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