Classical path from quantum motion for a particle in a transparent box
Autor(a) principal: | |
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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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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 |
_version_ |
1752122422177300480 |