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.
Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas
Materia
Física
Fine structure
Kronecker product
Matrix product
NMR spectrum
Operator product
Spin systems
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/98036
Acceder
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spelling The Kronecker product and some of its physical applicationsFernández, Francisco MarceloFísicaFine structureKronecker productMatrix productNMR spectrumOperator productSpin systemsIn 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.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas2016-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf65403-65414http://sedici.unlp.edu.ar/handle/10915/98036enginfo:eu-repo/semantics/altIdentifier/url/https://ri.conicet.gov.ar/11336/62295info:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/article/10.1088/0143-0807/37/6/065403/metainfo:eu-repo/semantics/altIdentifier/issn/0143-0807info:eu-repo/semantics/altIdentifier/doi/10.1088/0143-0807/37/6/065403info:eu-repo/semantics/altIdentifier/hdl/11336/62295info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-10-22T17:01:06Zoai:sedici.unlp.edu.ar:10915/98036Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-22 17:01:06.614SEDICI (UNLP) - Universidad Nacional de La Platafalse
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
Física
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 Física
Fine structure
Kronecker product
Matrix product
NMR spectrum
Operator product
Spin systems
topic Física
Fine structure
Kronecker product
Matrix product
NMR spectrum
Operator product
Spin systems
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.
Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas
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
Articulo
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
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status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/98036
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dc.language.none.fl_str_mv eng
language eng
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info:eu-repo/semantics/altIdentifier/issn/0143-0807
info:eu-repo/semantics/altIdentifier/doi/10.1088/0143-0807/37/6/065403
info:eu-repo/semantics/altIdentifier/hdl/11336/62295
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
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Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
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