Simple one-dimensional quantum-mechanical model for a particle attached to a surface

Autores
Fernández, Francisco Marcelo
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We present a simple one-dimensional quantum-mechanical model for a particle attached to a surface. It leads to the Schrodinger equation for a harmonic ¨ oscillator bounded on one side that we solve in terms of Weber functions and discuss the behaviour of the eigenvalues and eigenfunctions. We derive the virial theorem and other exact relationships as well as the asymptotic behaviour of the eigenvalues. We calculate the zero-point energy for model parameters corresponding to H adsorbed on Pd(1 0 0). The model is suitable for an advanced undergraduate or graduate course on quantum mechanics.
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
Oscillator
Surface
Adsorption
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:11336/279838
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Simple one-dimensional quantum-mechanical model for a particle attached to a surfaceFernández, Francisco MarceloOscillatorSurfaceAdsorptionhttps://purl.org/becyt/ford/1.4https://purl.org/becyt/ford/1We present a simple one-dimensional quantum-mechanical model for a particle attached to a surface. It leads to the Schrodinger equation for a harmonic ¨ oscillator bounded on one side that we solve in terms of Weber functions and discuss the behaviour of the eigenvalues and eigenfunctions. We derive the virial theorem and other exact relationships as well as the asymptotic behaviour of the eigenvalues. We calculate the zero-point energy for model parameters corresponding to H adsorbed on Pd(1 0 0). The model is suitable for an advanced undergraduate or graduate course on quantum mechanics.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 Publishing2010-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/279838Fernández, Francisco Marcelo; Simple one-dimensional quantum-mechanical model for a particle attached to a surface; IOP Publishing; European Journal of Physics; 31; 4; 6-2010; 961-9670143-0807CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://iopscience.iop.org/article/10.1088/0143-0807/31/4/025info:eu-repo/semantics/altIdentifier/doi/10.1088/0143-0807/31/4/025info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2026-02-06T12:14:27Zoai:ri.conicet.gov.ar:11336/279838instacron: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:34982026-02-06 12:14:27.816CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Simple one-dimensional quantum-mechanical model for a particle attached to a surface
title Simple one-dimensional quantum-mechanical model for a particle attached to a surface
spellingShingle Simple one-dimensional quantum-mechanical model for a particle attached to a surface
Fernández, Francisco Marcelo
Oscillator
Surface
Adsorption
title_short Simple one-dimensional quantum-mechanical model for a particle attached to a surface
title_full Simple one-dimensional quantum-mechanical model for a particle attached to a surface
title_fullStr Simple one-dimensional quantum-mechanical model for a particle attached to a surface
title_full_unstemmed Simple one-dimensional quantum-mechanical model for a particle attached to a surface
title_sort Simple one-dimensional quantum-mechanical model for a particle attached to a surface
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 Oscillator
Surface
Adsorption
topic Oscillator
Surface
Adsorption
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.4
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We present a simple one-dimensional quantum-mechanical model for a particle attached to a surface. It leads to the Schrodinger equation for a harmonic ¨ oscillator bounded on one side that we solve in terms of Weber functions and discuss the behaviour of the eigenvalues and eigenfunctions. We derive the virial theorem and other exact relationships as well as the asymptotic behaviour of the eigenvalues. We calculate the zero-point energy for model parameters corresponding to H adsorbed on Pd(1 0 0). The model is suitable for an advanced undergraduate or graduate course on quantum mechanics.
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 We present a simple one-dimensional quantum-mechanical model for a particle attached to a surface. It leads to the Schrodinger equation for a harmonic ¨ oscillator bounded on one side that we solve in terms of Weber functions and discuss the behaviour of the eigenvalues and eigenfunctions. We derive the virial theorem and other exact relationships as well as the asymptotic behaviour of the eigenvalues. We calculate the zero-point energy for model parameters corresponding to H adsorbed on Pd(1 0 0). The model is suitable for an advanced undergraduate or graduate course on quantum mechanics.
publishDate 2010
dc.date.none.fl_str_mv 2010-06
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/11336/279838
Fernández, Francisco Marcelo; Simple one-dimensional quantum-mechanical model for a particle attached to a surface; IOP Publishing; European Journal of Physics; 31; 4; 6-2010; 961-967
0143-0807
CONICET Digital
CONICET
url http://hdl.handle.net/11336/279838
identifier_str_mv Fernández, Francisco Marcelo; Simple one-dimensional quantum-mechanical model for a particle attached to a surface; IOP Publishing; European Journal of Physics; 31; 4; 6-2010; 961-967
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/url/https://iopscience.iop.org/article/10.1088/0143-0807/31/4/025
info:eu-repo/semantics/altIdentifier/doi/10.1088/0143-0807/31/4/025
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 13.106097

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