Solution of the quantum harmonic oscillator plus a delta-function potential at the origin: The oddness of its even-parity solutions
Autor(a) principal: | |
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Data de Publicação: | 2011 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/1822/61839 |
Resumo: | We derive the energy levels associated with the even-parity wavefunctions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the boundary conditions at the origin. This problem calls the attention of the students to an inaccurate statement in quantum mechanics textbooks often found in the context of the solution of the harmonic oscillator problem. |
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Solution of the quantum harmonic oscillator plus a delta-function potential at the origin: The oddness of its even-parity solutionsCiências Naturais::Ciências FísicasSocial SciencesScience & TechnologyWe derive the energy levels associated with the even-parity wavefunctions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the boundary conditions at the origin. This problem calls the attention of the students to an inaccurate statement in quantum mechanics textbooks often found in the context of the solution of the harmonic oscillator problem.IOP PublishingUniversidade do MinhoViana-Gomes, J.Peres, N. M. R.20112011-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/61839engJ Viana-Gomes and N M R Peres 2011 Eur. J. Phys. 32 13770143-08071361-640410.1088/0143-0807/32/5/025info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:24:10Zoai:repositorium.sdum.uminho.pt:1822/61839Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:18:05.118986Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Solution of the quantum harmonic oscillator plus a delta-function potential at the origin: The oddness of its even-parity solutions |
title |
Solution of the quantum harmonic oscillator plus a delta-function potential at the origin: The oddness of its even-parity solutions |
spellingShingle |
Solution of the quantum harmonic oscillator plus a delta-function potential at the origin: The oddness of its even-parity solutions Viana-Gomes, J. Ciências Naturais::Ciências Físicas Social Sciences Science & Technology |
title_short |
Solution of the quantum harmonic oscillator plus a delta-function potential at the origin: The oddness of its even-parity solutions |
title_full |
Solution of the quantum harmonic oscillator plus a delta-function potential at the origin: The oddness of its even-parity solutions |
title_fullStr |
Solution of the quantum harmonic oscillator plus a delta-function potential at the origin: The oddness of its even-parity solutions |
title_full_unstemmed |
Solution of the quantum harmonic oscillator plus a delta-function potential at the origin: The oddness of its even-parity solutions |
title_sort |
Solution of the quantum harmonic oscillator plus a delta-function potential at the origin: The oddness of its even-parity solutions |
author |
Viana-Gomes, J. |
author_facet |
Viana-Gomes, J. Peres, N. M. R. |
author_role |
author |
author2 |
Peres, N. M. R. |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Viana-Gomes, J. Peres, N. M. R. |
dc.subject.por.fl_str_mv |
Ciências Naturais::Ciências Físicas Social Sciences Science & Technology |
topic |
Ciências Naturais::Ciências Físicas Social Sciences Science & Technology |
description |
We derive the energy levels associated with the even-parity wavefunctions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the boundary conditions at the origin. This problem calls the attention of the students to an inaccurate statement in quantum mechanics textbooks often found in the context of the solution of the harmonic oscillator problem. |
publishDate |
2011 |
dc.date.none.fl_str_mv |
2011 2011-01-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/1822/61839 |
url |
http://hdl.handle.net/1822/61839 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
J Viana-Gomes and N M R Peres 2011 Eur. J. Phys. 32 1377 0143-0807 1361-6404 10.1088/0143-0807/32/5/025 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
IOP Publishing |
publisher.none.fl_str_mv |
IOP Publishing |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799132635710095360 |