A quantum-mechanical anharmonic oscillator with a most interesting spectrum

Autores
Amore, Paolo; Fernández, Francisco Marcelo
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We revisit the problem posed by an anharmonic oscillator with a potential given by a polynomial function of the coordinate of degree six that depends on a parameter λ. The ground state can be obtained exactly and its energy E0 = 1 is independent of λ. This solution is valid only for λ > 0 because the eigenfunction is not square integrable otherwise. Here we show that the perturbation series for the expectation values are Padé and Borel–Padé summable for λ > 0. When λ < 0 the spectrum exhibits an infinite number of avoided crossings at each of which the eigenfunctions undergo dramatic changes in their spatial distribution that we analyse by means of the expectation values ⟨x2⟩.
Facultad de Ciencias Exactas
Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas
Materia
Ciencias Exactas
Química
anharmonic oscillator
quasi-exactly solvable
perturbation theory
Padé summation
avoided crossings
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:10915/109370
Acceder
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oai_identifier_str oai:sedici.unlp.edu.ar:10915/109370
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling A quantum-mechanical anharmonic oscillator with a most interesting spectrumAmore, PaoloFernández, Francisco MarceloCiencias ExactasQuímicaanharmonic oscillatorquasi-exactly solvableperturbation theoryPadé summationavoided crossingsWe revisit the problem posed by an anharmonic oscillator with a potential given by a polynomial function of the coordinate of degree six that depends on a parameter λ. The ground state can be obtained exactly and its energy E<sub>0</sub> = 1 is independent of λ. This solution is valid only for λ > 0 because the eigenfunction is not square integrable otherwise. Here we show that the perturbation series for the expectation values are Padé and Borel–Padé summable for λ > 0. When λ < 0 the spectrum exhibits an infinite number of avoided crossings at each of which the eigenfunctions undergo dramatic changes in their spatial distribution that we analyse by means of the expectation values ⟨x<sup>2</sup>⟩.Facultad de Ciencias ExactasInstituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas2017info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf1-9http://sedici.unlp.edu.ar/handle/10915/109370enginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0003491617301963info:eu-repo/semantics/altIdentifier/issn/0003-4916info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aop.2017.07.007info: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:UNLP2025-09-29T11:24:47Zoai:sedici.unlp.edu.ar:10915/109370Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:24:47.408SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv A quantum-mechanical anharmonic oscillator with a most interesting spectrum
title A quantum-mechanical anharmonic oscillator with a most interesting spectrum
spellingShingle A quantum-mechanical anharmonic oscillator with a most interesting spectrum
Amore, Paolo
Ciencias Exactas
Química
anharmonic oscillator
quasi-exactly solvable
perturbation theory
Padé summation
avoided crossings
title_short A quantum-mechanical anharmonic oscillator with a most interesting spectrum
title_full A quantum-mechanical anharmonic oscillator with a most interesting spectrum
title_fullStr A quantum-mechanical anharmonic oscillator with a most interesting spectrum
title_full_unstemmed A quantum-mechanical anharmonic oscillator with a most interesting spectrum
title_sort A quantum-mechanical anharmonic oscillator with a most interesting spectrum
dc.creator.none.fl_str_mv Amore, Paolo
Fernández, Francisco Marcelo
author Amore, Paolo
author_facet Amore, Paolo
Fernández, Francisco Marcelo
author_role author
author2 Fernández, Francisco Marcelo
author2_role author
dc.subject.none.fl_str_mv Ciencias Exactas
Química
anharmonic oscillator
quasi-exactly solvable
perturbation theory
Padé summation
avoided crossings
topic Ciencias Exactas
Química
anharmonic oscillator
quasi-exactly solvable
perturbation theory
Padé summation
avoided crossings
dc.description.none.fl_txt_mv We revisit the problem posed by an anharmonic oscillator with a potential given by a polynomial function of the coordinate of degree six that depends on a parameter λ. The ground state can be obtained exactly and its energy E<sub>0</sub> = 1 is independent of λ. This solution is valid only for λ > 0 because the eigenfunction is not square integrable otherwise. Here we show that the perturbation series for the expectation values are Padé and Borel–Padé summable for λ > 0. When λ < 0 the spectrum exhibits an infinite number of avoided crossings at each of which the eigenfunctions undergo dramatic changes in their spatial distribution that we analyse by means of the expectation values ⟨x<sup>2</sup>⟩.
Facultad de Ciencias Exactas
Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas
description We revisit the problem posed by an anharmonic oscillator with a potential given by a polynomial function of the coordinate of degree six that depends on a parameter λ. The ground state can be obtained exactly and its energy E<sub>0</sub> = 1 is independent of λ. This solution is valid only for λ > 0 because the eigenfunction is not square integrable otherwise. Here we show that the perturbation series for the expectation values are Padé and Borel–Padé summable for λ > 0. When λ < 0 the spectrum exhibits an infinite number of avoided crossings at each of which the eigenfunctions undergo dramatic changes in their spatial distribution that we analyse by means of the expectation values ⟨x<sup>2</sup>⟩.
publishDate 2017
dc.date.none.fl_str_mv 2017
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/10915/109370
url http://sedici.unlp.edu.ar/handle/10915/109370
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0003491617301963
info:eu-repo/semantics/altIdentifier/issn/0003-4916
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aop.2017.07.007
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
1-9
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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