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〉.
Fil: Amore, Paolo. Universidad de Colima; México
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
Avoided Crossings
Padé Summation
Perturbation Theory
Quasi-Exactly Solvable
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:11336/63793
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/63793
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A quantum-mechanical anharmonic oscillator with a most interesting spectrumAmore, PaoloFernández, Francisco MarceloAnharmonic OscillatorAvoided CrossingsPadé SummationPerturbation TheoryQuasi-Exactly Solvablehttps://purl.org/becyt/ford/1.4https://purl.org/becyt/ford/1We 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〉.Fil: Amore, Paolo. Universidad de Colima; MéxicoFil: 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 Science2017-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/63793Amore, Paolo; Fernández, Francisco Marcelo; A quantum-mechanical anharmonic oscillator with a most interesting spectrum; Academic Press Inc Elsevier Science; Annals of Physics (New York); 385; 10-2017; 1-90003-4916CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.aop.2017.07.007info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0003491617301963info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:35:18Zoai:ri.conicet.gov.ar:11336/63793instacron: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:34982025-09-29 09:35:19.051CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
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
Anharmonic Oscillator
Avoided Crossings
Padé Summation
Perturbation Theory
Quasi-Exactly Solvable
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 Anharmonic Oscillator
Avoided Crossings
Padé Summation
Perturbation Theory
Quasi-Exactly Solvable
topic Anharmonic Oscillator
Avoided Crossings
Padé Summation
Perturbation Theory
Quasi-Exactly Solvable
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.4
https://purl.org/becyt/ford/1
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 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〉.
Fil: Amore, Paolo. Universidad de Colima; México
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 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〉.
publishDate 2017
dc.date.none.fl_str_mv 2017-10
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/11336/63793
Amore, Paolo; Fernández, Francisco Marcelo; A quantum-mechanical anharmonic oscillator with a most interesting spectrum; Academic Press Inc Elsevier Science; Annals of Physics (New York); 385; 10-2017; 1-9
0003-4916
CONICET Digital
CONICET
url http://hdl.handle.net/11336/63793
identifier_str_mv Amore, Paolo; Fernández, Francisco Marcelo; A quantum-mechanical anharmonic oscillator with a most interesting spectrum; Academic Press Inc Elsevier Science; Annals of Physics (New York); 385; 10-2017; 1-9
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.2017.07.007
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0003491617301963
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
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
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score 13.070432

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