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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/180829
Ver los metadatos del registro completo
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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 |
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reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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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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13.13397 |