Exact solution of the compressed hydrogen atom

Autores
Ferreyra, Jorge Mario; Proetto, Cesar Ramon
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The exact solution to the problem of a hydrogen atom confined in a spherical well (CHA) is discussed; the standard results for the unconfined hydrogen atom (UHA) are recovered as the sphere size becomes large compared to the Bohr radius. The solutions are characterized by a set of three quantum numbers N (= 1, 2, 3,...), L (= 0, 1, 2,...), and M (= - L, - L + 1,..., L - 1, L), and the energy eigenvalues, in contrast to the situation in the UHA, depend on both N and L. All members of a given family n = N + L, however, evolve asymptotically toward the same energy level in the large-sphere limit, recovering the typical n2 degeneracy of the UHA. Besides numerically exact solutions for arbitrary sphere sizes, rigorous analytical approximations are provided for the physically relevant strong- and weak-confinement regimes. A conjecture concerning the ordering of the energy levels is rigorously confirmed. The validity of the virial theorem, Kato's cusp condition, and the role played by the density as an alternative basic variable for the case of the CHA are discussed. © 2013 American Association of Physics Teachers.
Fil: Ferreyra, Jorge Mario. Universidad Nacional de Tucumán. Facultad de Ciencias Exactas y Tecnología. Departamento de Física. Laboratorio de Física del Sólido; Argentina
Fil: Proetto, Cesar Ramon. Comisión Nacional de Energía Atómica. Gerencia del Área Investigaciones y Aplicaciones No Nucleares. Gerencia de Física (CAB). Grupo de Teoría de Sólidos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
atom
hydrogen
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:11336/180829

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spelling Exact solution of the compressed hydrogen atomFerreyra, Jorge MarioProetto, Cesar Ramonatomhydrogenhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The exact solution to the problem of a hydrogen atom confined in a spherical well (CHA) is discussed; the standard results for the unconfined hydrogen atom (UHA) are recovered as the sphere size becomes large compared to the Bohr radius. The solutions are characterized by a set of three quantum numbers N (= 1, 2, 3,...), L (= 0, 1, 2,...), and M (= - L, - L + 1,..., L - 1, L), and the energy eigenvalues, in contrast to the situation in the UHA, depend on both N and L. All members of a given family n = N + L, however, evolve asymptotically toward the same energy level in the large-sphere limit, recovering the typical n2 degeneracy of the UHA. Besides numerically exact solutions for arbitrary sphere sizes, rigorous analytical approximations are provided for the physically relevant strong- and weak-confinement regimes. A conjecture concerning the ordering of the energy levels is rigorously confirmed. The validity of the virial theorem, Kato's cusp condition, and the role played by the density as an alternative basic variable for the case of the CHA are discussed. © 2013 American Association of Physics Teachers.Fil: Ferreyra, Jorge Mario. Universidad Nacional de Tucumán. Facultad de Ciencias Exactas y Tecnología. Departamento de Física. Laboratorio de Física del Sólido; ArgentinaFil: Proetto, Cesar Ramon. Comisión Nacional de Energía Atómica. Gerencia del Área Investigaciones y Aplicaciones No Nucleares. Gerencia de Física (CAB). Grupo de Teoría de Sólidos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaAmerican Association of Physics Teachers2013-11info: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/11336/180829Ferreyra, Jorge Mario; Proetto, Cesar Ramon; Exact solution of the compressed hydrogen atom; American Association of Physics Teachers; American Journal of Physics; 81; 11; 11-2013; 860-8650002-9505CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1119/1.4820244info:eu-repo/semantics/altIdentifier/url/https://aapt.scitation.org/doi/10.1119/1.4820244info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:52:34Zoai:ri.conicet.gov.ar:11336/180829instacron: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 09:52:34.987CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Exact solution of the compressed hydrogen atom
title Exact solution of the compressed hydrogen atom
spellingShingle Exact solution of the compressed hydrogen atom
Ferreyra, Jorge Mario
atom
hydrogen
title_short Exact solution of the compressed hydrogen atom
title_full Exact solution of the compressed hydrogen atom
title_fullStr Exact solution of the compressed hydrogen atom
title_full_unstemmed Exact solution of the compressed hydrogen atom
title_sort Exact solution of the compressed hydrogen atom
dc.creator.none.fl_str_mv Ferreyra, Jorge Mario
Proetto, Cesar Ramon
author Ferreyra, Jorge Mario
author_facet Ferreyra, Jorge Mario
Proetto, Cesar Ramon
author_role author
author2 Proetto, Cesar Ramon
author2_role author
dc.subject.none.fl_str_mv atom
hydrogen
topic atom
hydrogen
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The exact solution to the problem of a hydrogen atom confined in a spherical well (CHA) is discussed; the standard results for the unconfined hydrogen atom (UHA) are recovered as the sphere size becomes large compared to the Bohr radius. The solutions are characterized by a set of three quantum numbers N (= 1, 2, 3,...), L (= 0, 1, 2,...), and M (= - L, - L + 1,..., L - 1, L), and the energy eigenvalues, in contrast to the situation in the UHA, depend on both N and L. All members of a given family n = N + L, however, evolve asymptotically toward the same energy level in the large-sphere limit, recovering the typical n2 degeneracy of the UHA. Besides numerically exact solutions for arbitrary sphere sizes, rigorous analytical approximations are provided for the physically relevant strong- and weak-confinement regimes. A conjecture concerning the ordering of the energy levels is rigorously confirmed. The validity of the virial theorem, Kato's cusp condition, and the role played by the density as an alternative basic variable for the case of the CHA are discussed. © 2013 American Association of Physics Teachers.
Fil: Ferreyra, Jorge Mario. Universidad Nacional de Tucumán. Facultad de Ciencias Exactas y Tecnología. Departamento de Física. Laboratorio de Física del Sólido; Argentina
Fil: Proetto, Cesar Ramon. Comisión Nacional de Energía Atómica. Gerencia del Área Investigaciones y Aplicaciones No Nucleares. Gerencia de Física (CAB). Grupo de Teoría de Sólidos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description The exact solution to the problem of a hydrogen atom confined in a spherical well (CHA) is discussed; the standard results for the unconfined hydrogen atom (UHA) are recovered as the sphere size becomes large compared to the Bohr radius. The solutions are characterized by a set of three quantum numbers N (= 1, 2, 3,...), L (= 0, 1, 2,...), and M (= - L, - L + 1,..., L - 1, L), and the energy eigenvalues, in contrast to the situation in the UHA, depend on both N and L. All members of a given family n = N + L, however, evolve asymptotically toward the same energy level in the large-sphere limit, recovering the typical n2 degeneracy of the UHA. Besides numerically exact solutions for arbitrary sphere sizes, rigorous analytical approximations are provided for the physically relevant strong- and weak-confinement regimes. A conjecture concerning the ordering of the energy levels is rigorously confirmed. The validity of the virial theorem, Kato's cusp condition, and the role played by the density as an alternative basic variable for the case of the CHA are discussed. © 2013 American Association of Physics Teachers.
publishDate 2013
dc.date.none.fl_str_mv 2013-11
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/11336/180829
Ferreyra, Jorge Mario; Proetto, Cesar Ramon; Exact solution of the compressed hydrogen atom; American Association of Physics Teachers; American Journal of Physics; 81; 11; 11-2013; 860-865
0002-9505
CONICET Digital
CONICET
url http://hdl.handle.net/11336/180829
identifier_str_mv Ferreyra, Jorge Mario; Proetto, Cesar Ramon; Exact solution of the compressed hydrogen atom; American Association of Physics Teachers; American Journal of Physics; 81; 11; 11-2013; 860-865
0002-9505
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1119/1.4820244
info:eu-repo/semantics/altIdentifier/url/https://aapt.scitation.org/doi/10.1119/1.4820244
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 American Association of Physics Teachers
publisher.none.fl_str_mv American Association of Physics Teachers
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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