On an energy-dependent quantum system with solutions in terms of a class of hypergeometric para-orthogonal polynomials on the unit circle

Detalhes bibliográficos
Autor(a) principal: Borrego-Morell, Jorge A.
Data de Publicação: 2020
Outros Autores: Bracciali, Cleonice F. [UNESP], Ranga, Alagacone Sri [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.3390/math8071161
http://hdl.handle.net/11449/200816
Resumo: We study an energy-dependent potential related to the Rosen-Morse potential. We give in closed-form the expression of a system of eigenfunctions of the Schrodinger operator in terms of a class of functions associated to a family of hypergeometric para-orthogonal polynomials on the unit circle. We also present modified relations of orthogonality and an asymptotic formula. Consequently, bound state solutions can be obtained for some values of the parameters that define the model. As a particular case, we obtain the symmetric trigonometric Rosen-Morse potential for which there exists an orthogonal basis of eigenstates in a Hilbert space. By comparing the existent solutions for the symmetric trigonometric Rosen-Morse potential, an identity involving Gegenbauer polynomials is obtained.
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spelling On an energy-dependent quantum system with solutions in terms of a class of hypergeometric para-orthogonal polynomials on the unit circleAsymptotic expansionsEnergy-dependent potentialHypergeometric functionsOrdinary differential equationsOrthogonal polynomialsSchrödinger equationWe study an energy-dependent potential related to the Rosen-Morse potential. We give in closed-form the expression of a system of eigenfunctions of the Schrodinger operator in terms of a class of functions associated to a family of hypergeometric para-orthogonal polynomials on the unit circle. We also present modified relations of orthogonality and an asymptotic formula. Consequently, bound state solutions can be obtained for some values of the parameters that define the model. As a particular case, we obtain the symmetric trigonometric Rosen-Morse potential for which there exists an orthogonal basis of eigenstates in a Hilbert space. By comparing the existent solutions for the symmetric trigonometric Rosen-Morse potential, an identity involving Gegenbauer polynomials is obtained.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Departamento de Matemática Campus Santa Cruz da Serra UFRJ-Universidade Federal do Rio de JaneiroDepartamento de Matemática Campus São José do Rio Preto UNESP-Universidade Estadual PaulistaDepartamento de Matemática Campus São José do Rio Preto UNESP-Universidade Estadual PaulistaFAPESP: 2016/09906-0CNPq: 304087/2018-1CNPq: 402939/2016-6Universidade Federal do Rio de Janeiro (UFRJ)Universidade Estadual Paulista (Unesp)Borrego-Morell, Jorge A.Bracciali, Cleonice F. [UNESP]Ranga, Alagacone Sri [UNESP]2020-12-12T02:16:50Z2020-12-12T02:16:50Z2020-07-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.3390/math8071161Mathematics, v. 8, n. 7, 2020.2227-7390http://hdl.handle.net/11449/20081610.3390/math80711612-s2.0-8508859184783003224526224670000-0002-6823-4204Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengMathematicsinfo:eu-repo/semantics/openAccess2022-02-09T11:14:44Zoai:repositorio.unesp.br:11449/200816Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T16:24:53.575466Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv On an energy-dependent quantum system with solutions in terms of a class of hypergeometric para-orthogonal polynomials on the unit circle
title On an energy-dependent quantum system with solutions in terms of a class of hypergeometric para-orthogonal polynomials on the unit circle
spellingShingle On an energy-dependent quantum system with solutions in terms of a class of hypergeometric para-orthogonal polynomials on the unit circle
Borrego-Morell, Jorge A.
Asymptotic expansions
Energy-dependent potential
Hypergeometric functions
Ordinary differential equations
Orthogonal polynomials
Schrödinger equation
title_short On an energy-dependent quantum system with solutions in terms of a class of hypergeometric para-orthogonal polynomials on the unit circle
title_full On an energy-dependent quantum system with solutions in terms of a class of hypergeometric para-orthogonal polynomials on the unit circle
title_fullStr On an energy-dependent quantum system with solutions in terms of a class of hypergeometric para-orthogonal polynomials on the unit circle
title_full_unstemmed On an energy-dependent quantum system with solutions in terms of a class of hypergeometric para-orthogonal polynomials on the unit circle
title_sort On an energy-dependent quantum system with solutions in terms of a class of hypergeometric para-orthogonal polynomials on the unit circle
author Borrego-Morell, Jorge A.
author_facet Borrego-Morell, Jorge A.
Bracciali, Cleonice F. [UNESP]
Ranga, Alagacone Sri [UNESP]
author_role author
author2 Bracciali, Cleonice F. [UNESP]
Ranga, Alagacone Sri [UNESP]
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Federal do Rio de Janeiro (UFRJ)
Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Borrego-Morell, Jorge A.
Bracciali, Cleonice F. [UNESP]
Ranga, Alagacone Sri [UNESP]
dc.subject.por.fl_str_mv Asymptotic expansions
Energy-dependent potential
Hypergeometric functions
Ordinary differential equations
Orthogonal polynomials
Schrödinger equation
topic Asymptotic expansions
Energy-dependent potential
Hypergeometric functions
Ordinary differential equations
Orthogonal polynomials
Schrödinger equation
description We study an energy-dependent potential related to the Rosen-Morse potential. We give in closed-form the expression of a system of eigenfunctions of the Schrodinger operator in terms of a class of functions associated to a family of hypergeometric para-orthogonal polynomials on the unit circle. We also present modified relations of orthogonality and an asymptotic formula. Consequently, bound state solutions can be obtained for some values of the parameters that define the model. As a particular case, we obtain the symmetric trigonometric Rosen-Morse potential for which there exists an orthogonal basis of eigenstates in a Hilbert space. By comparing the existent solutions for the symmetric trigonometric Rosen-Morse potential, an identity involving Gegenbauer polynomials is obtained.
publishDate 2020
dc.date.none.fl_str_mv 2020-12-12T02:16:50Z
2020-12-12T02:16:50Z
2020-07-01
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.3390/math8071161
Mathematics, v. 8, n. 7, 2020.
2227-7390
http://hdl.handle.net/11449/200816
10.3390/math8071161
2-s2.0-85088591847
8300322452622467
0000-0002-6823-4204
url http://dx.doi.org/10.3390/math8071161
http://hdl.handle.net/11449/200816
identifier_str_mv Mathematics, v. 8, n. 7, 2020.
2227-7390
10.3390/math8071161
2-s2.0-85088591847
8300322452622467
0000-0002-6823-4204
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Mathematics
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
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