Group theoretical analysis of a quantum-mechanical three-dimensional quartic anharmonic oscillator

Autores
Fernández, Francisco Marcelo
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This paper illustrates the application of group theory to a quantum-mechanical three-dimensional quartic anharmonic oscillator with Oh symmetry. It is shown that group theory predicts the degeneracy of the energy levels and facilitates the application of perturbation theory and the Rayleigh-Ritz variational method as well as the interpretation of the results in terms of the symmetry of the solutions. We show how to obtain suitable symmetry-adapted basis sets.
Fil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina
Materia
ANHARMONIC OSCILLATOR
GROUP THEORY
OH POINT GROUP
PERTURBATION THEORY
SYMMETRY-ADAPTED BASIS SET
VARIATIONAL METHOD
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:11336/48728
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/48728
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Group theoretical analysis of a quantum-mechanical three-dimensional quartic anharmonic oscillatorFernández, Francisco MarceloANHARMONIC OSCILLATORGROUP THEORYOH POINT GROUPPERTURBATION THEORYSYMMETRY-ADAPTED BASIS SETVARIATIONAL METHODhttps://purl.org/becyt/ford/1.4https://purl.org/becyt/ford/1This paper illustrates the application of group theory to a quantum-mechanical three-dimensional quartic anharmonic oscillator with Oh symmetry. It is shown that group theory predicts the degeneracy of the energy levels and facilitates the application of perturbation theory and the Rayleigh-Ritz variational method as well as the interpretation of the results in terms of the symmetry of the solutions. We show how to obtain suitable symmetry-adapted basis sets.Fil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; ArgentinaAcademic Press Inc Elsevier Science2015-05info: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/11336/48728Fernández, Francisco Marcelo; Group theoretical analysis of a quantum-mechanical three-dimensional quartic anharmonic oscillator; Academic Press Inc Elsevier Science; Annals of Physics (New York); 356; 5-2015; 149-1570003-4916CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.aop.2015.02.029info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0003491615000883info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1501.00975info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:55:26Zoai:ri.conicet.gov.ar:11336/48728instacron: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 09:55:26.728CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Group theoretical analysis of a quantum-mechanical three-dimensional quartic anharmonic oscillator
title Group theoretical analysis of a quantum-mechanical three-dimensional quartic anharmonic oscillator
spellingShingle Group theoretical analysis of a quantum-mechanical three-dimensional quartic anharmonic oscillator
Fernández, Francisco Marcelo
ANHARMONIC OSCILLATOR
GROUP THEORY
OH POINT GROUP
PERTURBATION THEORY
SYMMETRY-ADAPTED BASIS SET
VARIATIONAL METHOD
title_short Group theoretical analysis of a quantum-mechanical three-dimensional quartic anharmonic oscillator
title_full Group theoretical analysis of a quantum-mechanical three-dimensional quartic anharmonic oscillator
title_fullStr Group theoretical analysis of a quantum-mechanical three-dimensional quartic anharmonic oscillator
title_full_unstemmed Group theoretical analysis of a quantum-mechanical three-dimensional quartic anharmonic oscillator
title_sort Group theoretical analysis of a quantum-mechanical three-dimensional quartic anharmonic oscillator
dc.creator.none.fl_str_mv Fernández, Francisco Marcelo
author Fernández, Francisco Marcelo
author_facet Fernández, Francisco Marcelo
author_role author
dc.subject.none.fl_str_mv ANHARMONIC OSCILLATOR
GROUP THEORY
OH POINT GROUP
PERTURBATION THEORY
SYMMETRY-ADAPTED BASIS SET
VARIATIONAL METHOD
topic ANHARMONIC OSCILLATOR
GROUP THEORY
OH POINT GROUP
PERTURBATION THEORY
SYMMETRY-ADAPTED BASIS SET
VARIATIONAL METHOD
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.4
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv This paper illustrates the application of group theory to a quantum-mechanical three-dimensional quartic anharmonic oscillator with Oh symmetry. It is shown that group theory predicts the degeneracy of the energy levels and facilitates the application of perturbation theory and the Rayleigh-Ritz variational method as well as the interpretation of the results in terms of the symmetry of the solutions. We show how to obtain suitable symmetry-adapted basis sets.
Fil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina
description This paper illustrates the application of group theory to a quantum-mechanical three-dimensional quartic anharmonic oscillator with Oh symmetry. It is shown that group theory predicts the degeneracy of the energy levels and facilitates the application of perturbation theory and the Rayleigh-Ritz variational method as well as the interpretation of the results in terms of the symmetry of the solutions. We show how to obtain suitable symmetry-adapted basis sets.
publishDate 2015
dc.date.none.fl_str_mv 2015-05
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/11336/48728
Fernández, Francisco Marcelo; Group theoretical analysis of a quantum-mechanical three-dimensional quartic anharmonic oscillator; Academic Press Inc Elsevier Science; Annals of Physics (New York); 356; 5-2015; 149-157
0003-4916
CONICET Digital
CONICET
url http://hdl.handle.net/11336/48728
identifier_str_mv Fernández, Francisco Marcelo; Group theoretical analysis of a quantum-mechanical three-dimensional quartic anharmonic oscillator; Academic Press Inc Elsevier Science; Annals of Physics (New York); 356; 5-2015; 149-157
0003-4916
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aop.2015.02.029
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0003491615000883
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1501.00975
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
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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
_version_ 1842269343871664128
score 13.13397

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