On form-preserving transformations for the time-dependent Schrodinger equation

In this paper we point out a close connection between the Darboux transformation and the group of point transformations which preserve the form of the time-dependent Schroumldinger equation (TDSE). In our main result, we prove that any pair of time-dependent real potentials related by a Darboux tran...

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Detalles Bibliográficos
Autores: Finkel Morgenstern, Federico, González López, Artemio, Kamran, Niky, Rodríguez González, Miguel Ángel
Tipo de recurso: artículo
Fecha de publicación:1999
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/59670
Acceso en línea:https://hdl.handle.net/20.500.14352/59670
Access Level:acceso abierto
Palabra clave:51-73
Física-Modelos matemáticos
Física matemática
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spelling On form-preserving transformations for the time-dependent Schrodinger equationFinkel Morgenstern, FedericoGonzález López, ArtemioKamran, NikyRodríguez González, Miguel Ángel51-73Física-Modelos matemáticosFísica matemáticaIn this paper we point out a close connection between the Darboux transformation and the group of point transformations which preserve the form of the time-dependent Schroumldinger equation (TDSE). In our main result, we prove that any pair of time-dependent real potentials related by a Darboux transformation for the TDSE may be transformed by a suitable point transformation into a pair of time-independent potentials related by a usual Darboux transformation for the stationary Schroumldinger equation. Thus, any (real) potential solvable via a time-dependent Darboux transformation can alternatively be solved by applying an appropriate form-preserving point transformation of the TDSE to a time-independent potential. The pre-eminent role of the latter type of transformations in the solution of the TDSE is illustrated with a family of quasi-exactly solvable time-dependent anharmonic potentials.American Institute of PhysicsUniversidad Complutense de Madrid19991999-07-0119991999-07-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/59670reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/596702026-06-02T12:44:21Z
dc.title.none.fl_str_mv On form-preserving transformations for the time-dependent Schrodinger equation
title On form-preserving transformations for the time-dependent Schrodinger equation
spellingShingle On form-preserving transformations for the time-dependent Schrodinger equation
Finkel Morgenstern, Federico
51-73
Física-Modelos matemáticos
Física matemática
title_short On form-preserving transformations for the time-dependent Schrodinger equation
title_full On form-preserving transformations for the time-dependent Schrodinger equation
title_fullStr On form-preserving transformations for the time-dependent Schrodinger equation
title_full_unstemmed On form-preserving transformations for the time-dependent Schrodinger equation
title_sort On form-preserving transformations for the time-dependent Schrodinger equation
dc.creator.none.fl_str_mv Finkel Morgenstern, Federico
González López, Artemio
Kamran, Niky
Rodríguez González, Miguel Ángel
author Finkel Morgenstern, Federico
author_facet Finkel Morgenstern, Federico
González López, Artemio
Kamran, Niky
Rodríguez González, Miguel Ángel
author_role author
author2 González López, Artemio
Kamran, Niky
Rodríguez González, Miguel Ángel
author2_role author
author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 51-73
Física-Modelos matemáticos
Física matemática
topic 51-73
Física-Modelos matemáticos
Física matemática
description In this paper we point out a close connection between the Darboux transformation and the group of point transformations which preserve the form of the time-dependent Schroumldinger equation (TDSE). In our main result, we prove that any pair of time-dependent real potentials related by a Darboux transformation for the TDSE may be transformed by a suitable point transformation into a pair of time-independent potentials related by a usual Darboux transformation for the stationary Schroumldinger equation. Thus, any (real) potential solvable via a time-dependent Darboux transformation can alternatively be solved by applying an appropriate form-preserving point transformation of the TDSE to a time-independent potential. The pre-eminent role of the latter type of transformations in the solution of the TDSE is illustrated with a family of quasi-exactly solvable time-dependent anharmonic potentials.
publishDate 1999
dc.date.none.fl_str_mv 1999
1999-07-01
1999
1999-07-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/59670
url https://hdl.handle.net/20.500.14352/59670
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv American Institute of Physics
publisher.none.fl_str_mv American Institute of Physics
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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