Wavefunctions from energies: Applications in simple potentials

Autores
Mitnik, Dario Marcelo; Mitnik, Santiago A. H.
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A remarkable mathematical property—somehow hidden and recently rediscovered—allows obtaining the eigenvectors of a Hermitian matrix directly from their eigenvalues. This opens the possibility to get the wavefunctions from the spectrum, an elusive goal of many fields in physics. Here, the formula is assessed for simple potentials, recovering the theoretical wavefunctions within machine accuracy. A striking feature of this eigenvalue–eigenvector relation is that it does not require knowing any of the entries of the working matrix. However, it requires the knowledge of the eigenvalues of the minor matrices (in which a row and a column have been deleted from the original matrix). We found a pattern in these sub-matrix spectra, allowing us to get the eigenvectors analytically. The physical information hidden behind this pattern is analyzed.
Fil: Mitnik, Dario Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina
Fil: Mitnik, Santiago A. H.. Universidad Nacional de San Martín. Escuela de Política y Gobierno; Argentina
Materia
ATOMIC WAVEFUNCTIONS
NUMERICAL METHODS
EIGENVECTOR-EIGENVALUE IDENTITY
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/153012
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Wavefunctions from energies: Applications in simple potentialsMitnik, Dario MarceloMitnik, Santiago A. H.ATOMIC WAVEFUNCTIONSNUMERICAL METHODSEIGENVECTOR-EIGENVALUE IDENTITYhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1A remarkable mathematical property—somehow hidden and recently rediscovered—allows obtaining the eigenvectors of a Hermitian matrix directly from their eigenvalues. This opens the possibility to get the wavefunctions from the spectrum, an elusive goal of many fields in physics. Here, the formula is assessed for simple potentials, recovering the theoretical wavefunctions within machine accuracy. A striking feature of this eigenvalue–eigenvector relation is that it does not require knowing any of the entries of the working matrix. However, it requires the knowledge of the eigenvalues of the minor matrices (in which a row and a column have been deleted from the original matrix). We found a pattern in these sub-matrix spectra, allowing us to get the eigenvectors analytically. The physical information hidden behind this pattern is analyzed.Fil: Mitnik, Dario Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; ArgentinaFil: Mitnik, Santiago A. H.. Universidad Nacional de San Martín. Escuela de Política y Gobierno; ArgentinaAmerican Institute of Physics2020-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/153012Mitnik, Dario Marcelo; Mitnik, Santiago A. H.; Wavefunctions from energies: Applications in simple potentials; American Institute of Physics; Journal of Mathematical Physics; 61; 6; 6-2020; 1-110022-2488CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://aip.scitation.org/doi/10.1063/5.0011115info:eu-repo/semantics/altIdentifier/doi/10.1063/5.0011115info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:54:28Zoai:ri.conicet.gov.ar:11336/153012instacron: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 09:54:28.866CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Wavefunctions from energies: Applications in simple potentials
title Wavefunctions from energies: Applications in simple potentials
spellingShingle Wavefunctions from energies: Applications in simple potentials
Mitnik, Dario Marcelo
ATOMIC WAVEFUNCTIONS
NUMERICAL METHODS
EIGENVECTOR-EIGENVALUE IDENTITY
title_short Wavefunctions from energies: Applications in simple potentials
title_full Wavefunctions from energies: Applications in simple potentials
title_fullStr Wavefunctions from energies: Applications in simple potentials
title_full_unstemmed Wavefunctions from energies: Applications in simple potentials
title_sort Wavefunctions from energies: Applications in simple potentials
dc.creator.none.fl_str_mv Mitnik, Dario Marcelo
Mitnik, Santiago A. H.
author Mitnik, Dario Marcelo
author_facet Mitnik, Dario Marcelo
Mitnik, Santiago A. H.
author_role author
author2 Mitnik, Santiago A. H.
author2_role author
dc.subject.none.fl_str_mv ATOMIC WAVEFUNCTIONS
NUMERICAL METHODS
EIGENVECTOR-EIGENVALUE IDENTITY
topic ATOMIC WAVEFUNCTIONS
NUMERICAL METHODS
EIGENVECTOR-EIGENVALUE IDENTITY
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv A remarkable mathematical property—somehow hidden and recently rediscovered—allows obtaining the eigenvectors of a Hermitian matrix directly from their eigenvalues. This opens the possibility to get the wavefunctions from the spectrum, an elusive goal of many fields in physics. Here, the formula is assessed for simple potentials, recovering the theoretical wavefunctions within machine accuracy. A striking feature of this eigenvalue–eigenvector relation is that it does not require knowing any of the entries of the working matrix. However, it requires the knowledge of the eigenvalues of the minor matrices (in which a row and a column have been deleted from the original matrix). We found a pattern in these sub-matrix spectra, allowing us to get the eigenvectors analytically. The physical information hidden behind this pattern is analyzed.
Fil: Mitnik, Dario Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina
Fil: Mitnik, Santiago A. H.. Universidad Nacional de San Martín. Escuela de Política y Gobierno; Argentina
description A remarkable mathematical property—somehow hidden and recently rediscovered—allows obtaining the eigenvectors of a Hermitian matrix directly from their eigenvalues. This opens the possibility to get the wavefunctions from the spectrum, an elusive goal of many fields in physics. Here, the formula is assessed for simple potentials, recovering the theoretical wavefunctions within machine accuracy. A striking feature of this eigenvalue–eigenvector relation is that it does not require knowing any of the entries of the working matrix. However, it requires the knowledge of the eigenvalues of the minor matrices (in which a row and a column have been deleted from the original matrix). We found a pattern in these sub-matrix spectra, allowing us to get the eigenvectors analytically. The physical information hidden behind this pattern is analyzed.
publishDate 2020
dc.date.none.fl_str_mv 2020-06
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/11336/153012
Mitnik, Dario Marcelo; Mitnik, Santiago A. H.; Wavefunctions from energies: Applications in simple potentials; American Institute of Physics; Journal of Mathematical Physics; 61; 6; 6-2020; 1-11
0022-2488
CONICET Digital
CONICET
url http://hdl.handle.net/11336/153012
identifier_str_mv Mitnik, Dario Marcelo; Mitnik, Santiago A. H.; Wavefunctions from energies: Applications in simple potentials; American Institute of Physics; Journal of Mathematical Physics; 61; 6; 6-2020; 1-11
0022-2488
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://aip.scitation.org/doi/10.1063/5.0011115
info:eu-repo/semantics/altIdentifier/doi/10.1063/5.0011115
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Institute of Physics
publisher.none.fl_str_mv American Institute of Physics
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
_version_ 1844613654306095104
score 13.070432

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