Possible scenarios transgressing the nondegeneracy theorem

Detalhes bibliográficos
Autor(a) principal: Ramos, Luiz G.m. [UNESP]
Data de Publicação: 2023
Outros Autores: Castro, Antonio S. De [UNESP]
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1590/1806-9126-RBEF-2023-0018
http://hdl.handle.net/11449/244852
Resumo: In contrast to the nondegeneracy theorem, we present various scenarios in one-dimensional quantum mechanics that demonstrate how the Wronskian of two bound-state eigenfunctions with the same energy eigenvalue can be zero without implying that the eigenfunctions are linearly dependent. It is shown that the nondegeneracy theorem fails only when the potential makes different bound-state solutions corresponding to the same energy vanish at the singular point or region of singularity.
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spelling Possible scenarios transgressing the nondegeneracy theoremNondegeneracy theoremTwo-fold degeneracyLinearly independent eigenfunctionsIn contrast to the nondegeneracy theorem, we present various scenarios in one-dimensional quantum mechanics that demonstrate how the Wronskian of two bound-state eigenfunctions with the same energy eigenvalue can be zero without implying that the eigenfunctions are linearly dependent. It is shown that the nondegeneracy theorem fails only when the potential makes different bound-state solutions corresponding to the same energy vanish at the singular point or region of singularity.Universidade Estadual Paulista “Júlio de Mesquita Filho”, Departamento de FísicaUniversidade Estadual Paulista “Júlio de Mesquita Filho”, Departamento de FísicaSociedade Brasileira de FísicaUniversidade Estadual Paulista (UNESP)Ramos, Luiz G.m. [UNESP]Castro, Antonio S. De [UNESP]2023-07-29T11:14:54Z2023-07-29T11:14:54Z2023-05-29info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article-application/pdfhttp://dx.doi.org/10.1590/1806-9126-RBEF-2023-0018Revista Brasileira de Ensino de Física. Sociedade Brasileira de Física, v. 45, p. -, 2023.1806-11171806-9126http://hdl.handle.net/11449/24485210.1590/1806-9126-RBEF-2023-0018S1806-11172023000100426S1806-11172023000100426.pdfSciELOreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengRevista Brasileira de Ensino de Físicainfo:eu-repo/semantics/openAccess2023-11-26T06:10:26Zoai:repositorio.unesp.br:11449/244852Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T18:45:34.722370Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Possible scenarios transgressing the nondegeneracy theorem
title Possible scenarios transgressing the nondegeneracy theorem
spellingShingle Possible scenarios transgressing the nondegeneracy theorem
Ramos, Luiz G.m. [UNESP]
Nondegeneracy theorem
Two-fold degeneracy
Linearly independent eigenfunctions
title_short Possible scenarios transgressing the nondegeneracy theorem
title_full Possible scenarios transgressing the nondegeneracy theorem
title_fullStr Possible scenarios transgressing the nondegeneracy theorem
title_full_unstemmed Possible scenarios transgressing the nondegeneracy theorem
title_sort Possible scenarios transgressing the nondegeneracy theorem
author Ramos, Luiz G.m. [UNESP]
author_facet Ramos, Luiz G.m. [UNESP]
Castro, Antonio S. De [UNESP]
author_role author
author2 Castro, Antonio S. De [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Ramos, Luiz G.m. [UNESP]
Castro, Antonio S. De [UNESP]
dc.subject.por.fl_str_mv Nondegeneracy theorem
Two-fold degeneracy
Linearly independent eigenfunctions
topic Nondegeneracy theorem
Two-fold degeneracy
Linearly independent eigenfunctions
description In contrast to the nondegeneracy theorem, we present various scenarios in one-dimensional quantum mechanics that demonstrate how the Wronskian of two bound-state eigenfunctions with the same energy eigenvalue can be zero without implying that the eigenfunctions are linearly dependent. It is shown that the nondegeneracy theorem fails only when the potential makes different bound-state solutions corresponding to the same energy vanish at the singular point or region of singularity.
publishDate 2023
dc.date.none.fl_str_mv 2023-07-29T11:14:54Z
2023-07-29T11:14:54Z
2023-05-29
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://dx.doi.org/10.1590/1806-9126-RBEF-2023-0018
Revista Brasileira de Ensino de Física. Sociedade Brasileira de Física, v. 45, p. -, 2023.
1806-1117
1806-9126
http://hdl.handle.net/11449/244852
10.1590/1806-9126-RBEF-2023-0018
S1806-11172023000100426
S1806-11172023000100426.pdf
url http://dx.doi.org/10.1590/1806-9126-RBEF-2023-0018
http://hdl.handle.net/11449/244852
identifier_str_mv Revista Brasileira de Ensino de Física. Sociedade Brasileira de Física, v. 45, p. -, 2023.
1806-1117
1806-9126
10.1590/1806-9126-RBEF-2023-0018
S1806-11172023000100426
S1806-11172023000100426.pdf
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Revista Brasileira de Ensino de Física
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 Sociedade Brasileira de Física
publisher.none.fl_str_mv Sociedade Brasileira de Física
dc.source.none.fl_str_mv SciELO
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1808128974566457344

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