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.
Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas
Materia
Física
Anharmonic oscillator
Group theory
Oh point group
Perturbation theory
Symmetry-adapted basis set
Variational method
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/99429
Acceder
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oai_identifier_str oai:sedici.unlp.edu.ar:10915/99429
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling Group theoretical analysis of a quantum-mechanical three-dimensional quartic anharmonic oscillatorFernández, Francisco MarceloFísicaAnharmonic oscillatorGroup theoryOh point groupPerturbation theorySymmetry-adapted basis setVariational methodThis 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.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas2015-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf149-157http://sedici.unlp.edu.ar/handle/10915/99429enginfo:eu-repo/semantics/altIdentifier/url/https://ri.conicet.gov.ar/11336/48728info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1501.00975info:eu-repo/semantics/altIdentifier/issn/0003-4916info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aop.2015.02.029info:eu-repo/semantics/altIdentifier/arxiv/1501.00975info:eu-repo/semantics/altIdentifier/hdl/11336/48728info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-03T10:52:20Zoai:sedici.unlp.edu.ar:10915/99429Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-03 10:52:21.237SEDICI (UNLP) - Universidad Nacional de La Platafalse
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
Física
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 Física
Anharmonic oscillator
Group theory
Oh point group
Perturbation theory
Symmetry-adapted basis set
Variational method
topic Física
Anharmonic oscillator
Group theory
Oh point group
Perturbation theory
Symmetry-adapted basis set
Variational method
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.
Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas
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
Articulo
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://sedici.unlp.edu.ar/handle/10915/99429
url http://sedici.unlp.edu.ar/handle/10915/99429
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://ri.conicet.gov.ar/11336/48728
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1501.00975
info:eu-repo/semantics/altIdentifier/issn/0003-4916
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aop.2015.02.029
info:eu-repo/semantics/altIdentifier/arxiv/1501.00975
info:eu-repo/semantics/altIdentifier/hdl/11336/48728
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
149-157
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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