Local approximation to the critical parameters of quantum wells

Autores
Fernández, Francisco Marcelo; Garcia, Javier
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We calculate the critical parameters for some simple quantum wells by means of the Riccati–Padé method. The original approach converges reasonably well for nonzero angular-momentum quantum number l but rather too slowly for the s states. We therefore propose a simple modification that yields remarkably accurate results for the latter case. The rate of convergence of both methods increases with l and decreases with the radial quantum number n. We compare RPM results with WKB ones for sufficiently large values of l. As illustrative examples we choose the one-dimensional and central-field Gaussian wells as well as the Yukawa potential. The application of perturbation theory by means of the RPM to a class of rational potentials yields interesting and baffling unphysical results.
Fil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina
Fil: Garcia, Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina
Materia
Quantum Wells
Critical Parameters
Riccati-Padé Method
Perturbation Theory
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/4816
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/4816
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Local approximation to the critical parameters of quantum wellsFernández, Francisco MarceloGarcia, JavierQuantum WellsCritical ParametersRiccati-Padé MethodPerturbation Theoryhttps://purl.org/becyt/ford/1.4https://purl.org/becyt/ford/1We calculate the critical parameters for some simple quantum wells by means of the Riccati–Padé method. The original approach converges reasonably well for nonzero angular-momentum quantum number l but rather too slowly for the s states. We therefore propose a simple modification that yields remarkably accurate results for the latter case. The rate of convergence of both methods increases with l and decreases with the radial quantum number n. We compare RPM results with WKB ones for sufficiently large values of l. As illustrative examples we choose the one-dimensional and central-field Gaussian wells as well as the Yukawa potential. The application of perturbation theory by means of the RPM to a class of rational potentials yields interesting and baffling unphysical results.Fil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; ArgentinaFil: Garcia, Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; ArgentinaElsevier2013-07-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/4816Fernández, Francisco Marcelo; Garcia, Javier; Local approximation to the critical parameters of quantum wells; Elsevier; Applied Mathematics And Computation; 220; 12-7-2013; 580-5920096-3003enginfo:eu-repo/semantics/altIdentifier/url/http://arxiv.org/abs/1210.4205info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0096300313006887info:eu-repo/semantics/altIdentifier/doi/10.1016/j.amc.2013.06.049info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:24:20Zoai:ri.conicet.gov.ar:11336/4816instacron: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:34982025-09-10 13:24:20.511CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Local approximation to the critical parameters of quantum wells
title Local approximation to the critical parameters of quantum wells
spellingShingle Local approximation to the critical parameters of quantum wells
Fernández, Francisco Marcelo
Quantum Wells
Critical Parameters
Riccati-Padé Method
Perturbation Theory
title_short Local approximation to the critical parameters of quantum wells
title_full Local approximation to the critical parameters of quantum wells
title_fullStr Local approximation to the critical parameters of quantum wells
title_full_unstemmed Local approximation to the critical parameters of quantum wells
title_sort Local approximation to the critical parameters of quantum wells
dc.creator.none.fl_str_mv Fernández, Francisco Marcelo
Garcia, Javier
author Fernández, Francisco Marcelo
author_facet Fernández, Francisco Marcelo
Garcia, Javier
author_role author
author2 Garcia, Javier
author2_role author
dc.subject.none.fl_str_mv Quantum Wells
Critical Parameters
Riccati-Padé Method
Perturbation Theory
topic Quantum Wells
Critical Parameters
Riccati-Padé Method
Perturbation Theory
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 calculate the critical parameters for some simple quantum wells by means of the Riccati–Padé method. The original approach converges reasonably well for nonzero angular-momentum quantum number l but rather too slowly for the s states. We therefore propose a simple modification that yields remarkably accurate results for the latter case. The rate of convergence of both methods increases with l and decreases with the radial quantum number n. We compare RPM results with WKB ones for sufficiently large values of l. As illustrative examples we choose the one-dimensional and central-field Gaussian wells as well as the Yukawa potential. The application of perturbation theory by means of the RPM to a class of rational potentials yields interesting and baffling unphysical results.
Fil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina
Fil: Garcia, Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina
description We calculate the critical parameters for some simple quantum wells by means of the Riccati–Padé method. The original approach converges reasonably well for nonzero angular-momentum quantum number l but rather too slowly for the s states. We therefore propose a simple modification that yields remarkably accurate results for the latter case. The rate of convergence of both methods increases with l and decreases with the radial quantum number n. We compare RPM results with WKB ones for sufficiently large values of l. As illustrative examples we choose the one-dimensional and central-field Gaussian wells as well as the Yukawa potential. The application of perturbation theory by means of the RPM to a class of rational potentials yields interesting and baffling unphysical results.
publishDate 2013
dc.date.none.fl_str_mv 2013-07-12
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/11336/4816
Fernández, Francisco Marcelo; Garcia, Javier; Local approximation to the critical parameters of quantum wells; Elsevier; Applied Mathematics And Computation; 220; 12-7-2013; 580-592
0096-3003
url http://hdl.handle.net/11336/4816
identifier_str_mv Fernández, Francisco Marcelo; Garcia, Javier; Local approximation to the critical parameters of quantum wells; Elsevier; Applied Mathematics And Computation; 220; 12-7-2013; 580-592
0096-3003
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://arxiv.org/abs/1210.4205
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0096300313006887
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.amc.2013.06.049
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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 12.48226

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