Unusual situations that arise with the Dirac delta function and its derivative
Autor(a) principal: | |
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Data de Publicação: | 2009 |
Outros Autores: | , |
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=S1806-11172009000400004 |
Resumo: | There is a situation such that, when a function (<img src="/img/revistas/rbef/v31n4/a04x.gif" align="absmiddle">) is combined with the Dirac delta function δ(<img src="/img/revistas/rbef/v31n4/a04x.gif" align="absmiddle">), the usual formula <img src="/img/revistas/rbef/v31n4/a04form01.gif" align="absmiddle">does not hold. A similar situation may also be encountered with the derivative of the delta function δ'(<img src="/img/revistas/rbef/v31n4/a04x.gif" align="absmiddle">), regarding the validity of <img src="/img/revistas/rbef/v31n4/a04form02.gif" align="absmiddle">. We present an overview of such unusual situations and elucidate their underlying mechanisms. We discuss implications of the situations regarding the transmission-reflection problem of one-dimensional quantum mechanics. |
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Unusual situations that arise with the Dirac delta function and its derivativeDirac delta functionsingular functionsquantum mechanicsThere is a situation such that, when a function (<img src="/img/revistas/rbef/v31n4/a04x.gif" align="absmiddle">) is combined with the Dirac delta function δ(<img src="/img/revistas/rbef/v31n4/a04x.gif" align="absmiddle">), the usual formula <img src="/img/revistas/rbef/v31n4/a04form01.gif" align="absmiddle">does not hold. A similar situation may also be encountered with the derivative of the delta function δ'(<img src="/img/revistas/rbef/v31n4/a04x.gif" align="absmiddle">), regarding the validity of <img src="/img/revistas/rbef/v31n4/a04form02.gif" align="absmiddle">. We present an overview of such unusual situations and elucidate their underlying mechanisms. We discuss implications of the situations regarding the transmission-reflection problem of one-dimensional quantum mechanics.Sociedade Brasileira de Física2009-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172009000400004Revista Brasileira de Ensino de Física v.31 n.4 2009reponame:Revista Brasileira de Ensino de Física (Online)instname:Sociedade Brasileira de Física (SBF)instacron:SBF10.1590/S1806-11172009000400004info:eu-repo/semantics/openAccessCoutinho,F.A.BNogami,YToyama,F.Meng2010-04-26T00:00:00Zoai:scielo:S1806-11172009000400004Revistahttp://www.sbfisica.org.br/rbef/https://old.scielo.br/oai/scielo-oai.php||marcio@sbfisica.org.br1806-91261806-1117opendoar:2010-04-26T00:00Revista Brasileira de Ensino de Física (Online) - Sociedade Brasileira de Física (SBF)false |
dc.title.none.fl_str_mv |
Unusual situations that arise with the Dirac delta function and its derivative |
title |
Unusual situations that arise with the Dirac delta function and its derivative |
spellingShingle |
Unusual situations that arise with the Dirac delta function and its derivative Coutinho,F.A.B Dirac delta function singular functions quantum mechanics |
title_short |
Unusual situations that arise with the Dirac delta function and its derivative |
title_full |
Unusual situations that arise with the Dirac delta function and its derivative |
title_fullStr |
Unusual situations that arise with the Dirac delta function and its derivative |
title_full_unstemmed |
Unusual situations that arise with the Dirac delta function and its derivative |
title_sort |
Unusual situations that arise with the Dirac delta function and its derivative |
author |
Coutinho,F.A.B |
author_facet |
Coutinho,F.A.B Nogami,Y Toyama,F.M |
author_role |
author |
author2 |
Nogami,Y Toyama,F.M |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Coutinho,F.A.B Nogami,Y Toyama,F.M |
dc.subject.por.fl_str_mv |
Dirac delta function singular functions quantum mechanics |
topic |
Dirac delta function singular functions quantum mechanics |
description |
There is a situation such that, when a function (<img src="/img/revistas/rbef/v31n4/a04x.gif" align="absmiddle">) is combined with the Dirac delta function δ(<img src="/img/revistas/rbef/v31n4/a04x.gif" align="absmiddle">), the usual formula <img src="/img/revistas/rbef/v31n4/a04form01.gif" align="absmiddle">does not hold. A similar situation may also be encountered with the derivative of the delta function δ'(<img src="/img/revistas/rbef/v31n4/a04x.gif" align="absmiddle">), regarding the validity of <img src="/img/revistas/rbef/v31n4/a04form02.gif" align="absmiddle">. We present an overview of such unusual situations and elucidate their underlying mechanisms. We discuss implications of the situations regarding the transmission-reflection problem of one-dimensional quantum mechanics. |
publishDate |
2009 |
dc.date.none.fl_str_mv |
2009-12-01 |
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=S1806-11172009000400004 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172009000400004 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S1806-11172009000400004 |
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.31 n.4 2009 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_ |
1752122420689371136 |