Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials

Autores
Amore, Paolo; Fernández, Francisco Marcelo
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We generalize a small-energy expansion for one-dimensional quantum-mechanical models proposed recently by other authors. The original approach was devised to treat symmetric potentials and here we show how to extend it to non-symmetric ones. Present approach is based on matching the logarithmic derivatives for the left and right solutions to the Schrödinger equation at the origin (or any other point chosen conveniently). As in the original method, each logarithmic derivative can be expanded in a small-energy series by straightforward perturbation theory. We test the new approach on four simple models, one of which is not exactly solvable. The perturbation expansion converges in all the illustrative examples so that one obtains the ground-state energy with an accuracy determined by the number of available perturbation corrections.
Fil: Amore, Paolo. Universidad de Colima. Facultad de Ciencias; México
Fil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina
Materia
ANHARMONIC OSCILLATOR
CONVERGENCE
FINITE WELLS
ONE-DIMENSIONAL SCHRÖDINGER EQUATION
SMALL-ENERGY SERIES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/82153
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentialsAmore, PaoloFernández, Francisco MarceloANHARMONIC OSCILLATORCONVERGENCEFINITE WELLSONE-DIMENSIONAL SCHRÖDINGER EQUATIONSMALL-ENERGY SERIEShttps://purl.org/becyt/ford/1.4https://purl.org/becyt/ford/1We generalize a small-energy expansion for one-dimensional quantum-mechanical models proposed recently by other authors. The original approach was devised to treat symmetric potentials and here we show how to extend it to non-symmetric ones. Present approach is based on matching the logarithmic derivatives for the left and right solutions to the Schrödinger equation at the origin (or any other point chosen conveniently). As in the original method, each logarithmic derivative can be expanded in a small-energy series by straightforward perturbation theory. We test the new approach on four simple models, one of which is not exactly solvable. The perturbation expansion converges in all the illustrative examples so that one obtains the ground-state energy with an accuracy determined by the number of available perturbation corrections.Fil: Amore, Paolo. Universidad de Colima. Facultad de Ciencias; MéxicoFil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; ArgentinaSpringer2015-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/82153Amore, Paolo; Fernández, Francisco Marcelo; Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials; Springer; Journal of Mathematical Chemistry; 53; 6; 6-2015; 1351-13620259-97911572-8897CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s10910-015-0492-8info:eu-repo/semantics/altIdentifier/doi/10.1007/s10910-015-0492-8info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1410.5813info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:52:39Zoai:ri.conicet.gov.ar:11336/82153instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:52:39.767CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials
title Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials
spellingShingle Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials
Amore, Paolo
ANHARMONIC OSCILLATOR
CONVERGENCE
FINITE WELLS
ONE-DIMENSIONAL SCHRÖDINGER EQUATION
SMALL-ENERGY SERIES
title_short Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials
title_full Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials
title_fullStr Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials
title_full_unstemmed Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials
title_sort Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials
dc.creator.none.fl_str_mv Amore, Paolo
Fernández, Francisco Marcelo
author Amore, Paolo
author_facet Amore, Paolo
Fernández, Francisco Marcelo
author_role author
author2 Fernández, Francisco Marcelo
author2_role author
dc.subject.none.fl_str_mv ANHARMONIC OSCILLATOR
CONVERGENCE
FINITE WELLS
ONE-DIMENSIONAL SCHRÖDINGER EQUATION
SMALL-ENERGY SERIES
topic ANHARMONIC OSCILLATOR
CONVERGENCE
FINITE WELLS
ONE-DIMENSIONAL SCHRÖDINGER EQUATION
SMALL-ENERGY SERIES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.4
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We generalize a small-energy expansion for one-dimensional quantum-mechanical models proposed recently by other authors. The original approach was devised to treat symmetric potentials and here we show how to extend it to non-symmetric ones. Present approach is based on matching the logarithmic derivatives for the left and right solutions to the Schrödinger equation at the origin (or any other point chosen conveniently). As in the original method, each logarithmic derivative can be expanded in a small-energy series by straightforward perturbation theory. We test the new approach on four simple models, one of which is not exactly solvable. The perturbation expansion converges in all the illustrative examples so that one obtains the ground-state energy with an accuracy determined by the number of available perturbation corrections.
Fil: Amore, Paolo. Universidad de Colima. Facultad de Ciencias; México
Fil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina
description We generalize a small-energy expansion for one-dimensional quantum-mechanical models proposed recently by other authors. The original approach was devised to treat symmetric potentials and here we show how to extend it to non-symmetric ones. Present approach is based on matching the logarithmic derivatives for the left and right solutions to the Schrödinger equation at the origin (or any other point chosen conveniently). As in the original method, each logarithmic derivative can be expanded in a small-energy series by straightforward perturbation theory. We test the new approach on four simple models, one of which is not exactly solvable. The perturbation expansion converges in all the illustrative examples so that one obtains the ground-state energy with an accuracy determined by the number of available perturbation corrections.
publishDate 2015
dc.date.none.fl_str_mv 2015-06
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/82153
Amore, Paolo; Fernández, Francisco Marcelo; Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials; Springer; Journal of Mathematical Chemistry; 53; 6; 6-2015; 1351-1362
0259-9791
1572-8897
CONICET Digital
CONICET
url http://hdl.handle.net/11336/82153
identifier_str_mv Amore, Paolo; Fernández, Francisco Marcelo; Small-energy series for one-dimensional quantum-mechanical models with non-symmetric potentials; Springer; Journal of Mathematical Chemistry; 53; 6; 6-2015; 1351-1362
0259-9791
1572-8897
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s10910-015-0492-8
info:eu-repo/semantics/altIdentifier/doi/10.1007/s10910-015-0492-8
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1410.5813
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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