The Kronecker product and some of its physical applications

Autores
Fernández, Francisco Marcelo
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In a typical introductory course on quantum mechanics the student has to face two quite different operator products. One of them leads to, for example, commutators and the uncertainty principle, and the other appears when one goes from a one-particle system to a multi-particle one. The latter gives rise to the direct or tensor product of operators and vector spaces, and to the Kronecker product of the matrix representations of the operators. We illustrate the practical utility of the Kronecker product by means of two spin systems commonly discussed in introductory courses on quantum mechanics and also by means of a simple model for the interpretation of the NMR signal produced by two interacting protons.
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
FINE STRUCTURE
KRONECKER PRODUCT
MATRIX PRODUCT
NMR SPECTRUM
OPERATOR PRODUCT
SPIN SYSTEMS
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:11336/62295
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/62295
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network_name_str CONICET Digital (CONICET)
spelling The Kronecker product and some of its physical applicationsFernández, Francisco MarceloFINE STRUCTUREKRONECKER PRODUCTMATRIX PRODUCTNMR SPECTRUMOPERATOR PRODUCTSPIN SYSTEMShttps://purl.org/becyt/ford/1.4https://purl.org/becyt/ford/1In a typical introductory course on quantum mechanics the student has to face two quite different operator products. One of them leads to, for example, commutators and the uncertainty principle, and the other appears when one goes from a one-particle system to a multi-particle one. The latter gives rise to the direct or tensor product of operators and vector spaces, and to the Kronecker product of the matrix representations of the operators. We illustrate the practical utility of the Kronecker product by means of two spin systems commonly discussed in introductory courses on quantum mechanics and also by means of a simple model for the interpretation of the NMR signal produced by two interacting protons.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; ArgentinaIOP Publishing2016-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/62295Fernández, Francisco Marcelo; The Kronecker product and some of its physical applications; IOP Publishing; European Journal of Physics; 37; 6; 9-2016; 65403-654140143-0807CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1088/0143-0807/37/6/065403info:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/article/10.1088/0143-0807/37/6/065403/metainfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:19:08Zoai:ri.conicet.gov.ar:11336/62295instacron: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:34982025-10-22 11:19:08.296CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The Kronecker product and some of its physical applications
title The Kronecker product and some of its physical applications
spellingShingle The Kronecker product and some of its physical applications
Fernández, Francisco Marcelo
FINE STRUCTURE
KRONECKER PRODUCT
MATRIX PRODUCT
NMR SPECTRUM
OPERATOR PRODUCT
SPIN SYSTEMS
title_short The Kronecker product and some of its physical applications
title_full The Kronecker product and some of its physical applications
title_fullStr The Kronecker product and some of its physical applications
title_full_unstemmed The Kronecker product and some of its physical applications
title_sort The Kronecker product and some of its physical applications
dc.creator.none.fl_str_mv Fernández, Francisco Marcelo
author Fernández, Francisco Marcelo
author_facet Fernández, Francisco Marcelo
author_role author
dc.subject.none.fl_str_mv FINE STRUCTURE
KRONECKER PRODUCT
MATRIX PRODUCT
NMR SPECTRUM
OPERATOR PRODUCT
SPIN SYSTEMS
topic FINE STRUCTURE
KRONECKER PRODUCT
MATRIX PRODUCT
NMR SPECTRUM
OPERATOR PRODUCT
SPIN SYSTEMS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.4
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In a typical introductory course on quantum mechanics the student has to face two quite different operator products. One of them leads to, for example, commutators and the uncertainty principle, and the other appears when one goes from a one-particle system to a multi-particle one. The latter gives rise to the direct or tensor product of operators and vector spaces, and to the Kronecker product of the matrix representations of the operators. We illustrate the practical utility of the Kronecker product by means of two spin systems commonly discussed in introductory courses on quantum mechanics and also by means of a simple model for the interpretation of the NMR signal produced by two interacting protons.
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 In a typical introductory course on quantum mechanics the student has to face two quite different operator products. One of them leads to, for example, commutators and the uncertainty principle, and the other appears when one goes from a one-particle system to a multi-particle one. The latter gives rise to the direct or tensor product of operators and vector spaces, and to the Kronecker product of the matrix representations of the operators. We illustrate the practical utility of the Kronecker product by means of two spin systems commonly discussed in introductory courses on quantum mechanics and also by means of a simple model for the interpretation of the NMR signal produced by two interacting protons.
publishDate 2016
dc.date.none.fl_str_mv 2016-09
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/11336/62295
Fernández, Francisco Marcelo; The Kronecker product and some of its physical applications; IOP Publishing; European Journal of Physics; 37; 6; 9-2016; 65403-65414
0143-0807
CONICET Digital
CONICET
url http://hdl.handle.net/11336/62295
identifier_str_mv Fernández, Francisco Marcelo; The Kronecker product and some of its physical applications; IOP Publishing; European Journal of Physics; 37; 6; 9-2016; 65403-65414
0143-0807
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1088/0143-0807/37/6/065403
info:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/article/10.1088/0143-0807/37/6/065403/meta
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 IOP Publishing
publisher.none.fl_str_mv IOP Publishing
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 12.982451

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