A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces

Autores
Vignat, C.; Lamberti, Pedro Walter
Año de publicación
2009
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Recently, Cariñena, et al. Ann. Phys. 322, 434 2007 introduced a new family of orthogonal polynomials that appear in the wave functions of the quantum harmonic oscillator in two-dimensional constant curvature spaces. They are a generalization of the Hermite polynomials and will be called curved Hermite polynomials in the following. We show that these polynomials are naturally related to the relativistic Hermite polynomials introduced by Aldaya et al. Phys. Lett. A 156, 381 1991 , and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between the solutions of the quantum harmonic oscillator on negative curvature spaces and on positive curvature spaces. At last, we show a maximum entropy property for the ground states of these oscillators.
Fil: Vignat, C.. Université de Marne la Vallée; Francia
Fil: Lamberti, Pedro Walter. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
Materia
quantum harmonic oscillators
constant curvature spaces
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:11336/242081
Acceder
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network_name_str CONICET Digital (CONICET)
spelling A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spacesVignat, C.Lamberti, Pedro Walterquantum harmonic oscillatorsconstant curvature spaceshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1Recently, Cariñena, et al. Ann. Phys. 322, 434 2007 introduced a new family of orthogonal polynomials that appear in the wave functions of the quantum harmonic oscillator in two-dimensional constant curvature spaces. They are a generalization of the Hermite polynomials and will be called curved Hermite polynomials in the following. We show that these polynomials are naturally related to the relativistic Hermite polynomials introduced by Aldaya et al. Phys. Lett. A 156, 381 1991 , and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between the solutions of the quantum harmonic oscillator on negative curvature spaces and on positive curvature spaces. At last, we show a maximum entropy property for the ground states of these oscillators.Fil: Vignat, C.. Université de Marne la Vallée; FranciaFil: Lamberti, Pedro Walter. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaAmerican Institute of Physics2009-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/242081Vignat, C.; Lamberti, Pedro Walter; A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces; American Institute of Physics; Journal of Mathematical Physics; 50; 10; 10-2009; 1-100022-2488CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://pubs.aip.org/aip/jmp/article-abstract/50/10/103514/985166/A-study-of-the-orthogonal-polynomials-associated?redirectedFrom=fulltextinfo:eu-repo/semantics/altIdentifier/doi/10.1063/1.3227659info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:07:37Zoai:ri.conicet.gov.ar:11336/242081instacron: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 10:07:37.437CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces
title A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces
spellingShingle A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces
Vignat, C.
quantum harmonic oscillators
constant curvature spaces
title_short A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces
title_full A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces
title_fullStr A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces
title_full_unstemmed A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces
title_sort A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces
dc.creator.none.fl_str_mv Vignat, C.
Lamberti, Pedro Walter
author Vignat, C.
author_facet Vignat, C.
Lamberti, Pedro Walter
author_role author
author2 Lamberti, Pedro Walter
author2_role author
dc.subject.none.fl_str_mv quantum harmonic oscillators
constant curvature spaces
topic quantum harmonic oscillators
constant curvature spaces
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Recently, Cariñena, et al. Ann. Phys. 322, 434 2007 introduced a new family of orthogonal polynomials that appear in the wave functions of the quantum harmonic oscillator in two-dimensional constant curvature spaces. They are a generalization of the Hermite polynomials and will be called curved Hermite polynomials in the following. We show that these polynomials are naturally related to the relativistic Hermite polynomials introduced by Aldaya et al. Phys. Lett. A 156, 381 1991 , and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between the solutions of the quantum harmonic oscillator on negative curvature spaces and on positive curvature spaces. At last, we show a maximum entropy property for the ground states of these oscillators.
Fil: Vignat, C.. Université de Marne la Vallée; Francia
Fil: Lamberti, Pedro Walter. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
description Recently, Cariñena, et al. Ann. Phys. 322, 434 2007 introduced a new family of orthogonal polynomials that appear in the wave functions of the quantum harmonic oscillator in two-dimensional constant curvature spaces. They are a generalization of the Hermite polynomials and will be called curved Hermite polynomials in the following. We show that these polynomials are naturally related to the relativistic Hermite polynomials introduced by Aldaya et al. Phys. Lett. A 156, 381 1991 , and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between the solutions of the quantum harmonic oscillator on negative curvature spaces and on positive curvature spaces. At last, we show a maximum entropy property for the ground states of these oscillators.
publishDate 2009
dc.date.none.fl_str_mv 2009-10
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/11336/242081
Vignat, C.; Lamberti, Pedro Walter; A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces; American Institute of Physics; Journal of Mathematical Physics; 50; 10; 10-2009; 1-10
0022-2488
CONICET Digital
CONICET
url http://hdl.handle.net/11336/242081
identifier_str_mv Vignat, C.; Lamberti, Pedro Walter; A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces; American Institute of Physics; Journal of Mathematical Physics; 50; 10; 10-2009; 1-10
0022-2488
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://pubs.aip.org/aip/jmp/article-abstract/50/10/103514/985166/A-study-of-the-orthogonal-polynomials-associated?redirectedFrom=fulltext
info:eu-repo/semantics/altIdentifier/doi/10.1063/1.3227659
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
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: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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