Classical path from quantum motion for a particle in a transparent box

Detalhes bibliográficos
Autor(a) principal: Vincenzo,Salvatore De
Data de Publicação: 2014
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Revista Brasileira de Ensino de Física (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172014000200013
Resumo: We consider the problem of a free particle inside a one-dimensional box with transparent walls (or equivalently, along a circle with a constant speed) and discuss the classical and quantum descriptions of the problem. After calculating the mean value of the position operator in a time-dependent normalized complex general state and the Fourier series of the function position, we explicitly prove that these two quantities are in accordance by (essentially) imposing the approximation of high principal quantum numbers on the mean value. The presentation is accessible to advanced undergraduate students with a knowledge of the basic ideas of quantum mechanics.
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spelling Classical path from quantum motion for a particle in a transparent boxcorrespondence principleclassical limitEhrenfest theoremWe consider the problem of a free particle inside a one-dimensional box with transparent walls (or equivalently, along a circle with a constant speed) and discuss the classical and quantum descriptions of the problem. After calculating the mean value of the position operator in a time-dependent normalized complex general state and the Fourier series of the function position, we explicitly prove that these two quantities are in accordance by (essentially) imposing the approximation of high principal quantum numbers on the mean value. The presentation is accessible to advanced undergraduate students with a knowledge of the basic ideas of quantum mechanics.Sociedade Brasileira de Física2014-06-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172014000200013Revista Brasileira de Ensino de Física v.36 n.2 2014reponame:Revista Brasileira de Ensino de Física (Online)instname:Sociedade Brasileira de Física (SBF)instacron:SBF10.1590/S1806-11172014000200013info:eu-repo/semantics/openAccessVincenzo,Salvatore Deeng2014-07-03T00:00:00Zoai:scielo:S1806-11172014000200013Revistahttp://www.sbfisica.org.br/rbef/https://old.scielo.br/oai/scielo-oai.php||marcio@sbfisica.org.br1806-91261806-1117opendoar:2014-07-03T00:00Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)false
dc.title.none.fl_str_mv Classical path from quantum motion for a particle in a transparent box
title Classical path from quantum motion for a particle in a transparent box
spellingShingle Classical path from quantum motion for a particle in a transparent box
Vincenzo,Salvatore De
correspondence principle
classical limit
Ehrenfest theorem
title_short Classical path from quantum motion for a particle in a transparent box
title_full Classical path from quantum motion for a particle in a transparent box
title_fullStr Classical path from quantum motion for a particle in a transparent box
title_full_unstemmed Classical path from quantum motion for a particle in a transparent box
title_sort Classical path from quantum motion for a particle in a transparent box
author Vincenzo,Salvatore De
author_facet Vincenzo,Salvatore De
author_role author
dc.contributor.author.fl_str_mv Vincenzo,Salvatore De
dc.subject.por.fl_str_mv correspondence principle
classical limit
Ehrenfest theorem
topic correspondence principle
classical limit
Ehrenfest theorem
description We consider the problem of a free particle inside a one-dimensional box with transparent walls (or equivalently, along a circle with a constant speed) and discuss the classical and quantum descriptions of the problem. After calculating the mean value of the position operator in a time-dependent normalized complex general state and the Fourier series of the function position, we explicitly prove that these two quantities are in accordance by (essentially) imposing the approximation of high principal quantum numbers on the mean value. The presentation is accessible to advanced undergraduate students with a knowledge of the basic ideas of quantum mechanics.
publishDate 2014
dc.date.none.fl_str_mv 2014-06-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172014000200013
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172014000200013
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S1806-11172014000200013
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
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 Revista Brasileira de Ensino de Física v.36 n.2 2014
reponame:Revista Brasileira de Ensino de Física (Online)
instname:Sociedade Brasileira de Física (SBF)
instacron:SBF
instname_str Sociedade Brasileira de Física (SBF)
instacron_str SBF
institution SBF
reponame_str Revista Brasileira de Ensino de Física (Online)
collection Revista Brasileira de Ensino de Física (Online)
repository.name.fl_str_mv Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)
repository.mail.fl_str_mv ||marcio@sbfisica.org.br
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