Variational approach to the Schrödinger equation with a delta-function potential
- Autores
- Fernández, Francisco Marcelo
- Año de publicación
- 2022
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We obtain accurate eigenvalues of the one-dimensional Schrödinger equation with a Hamiltonian of the form H g = H + gd(x), where d(x) is the Dirac delta function. We show that the well known Rayleigh-Ritz variational method is a suitable approach provided that the basis set takes into account the effect of the Dirac delta on the wavefunction. Present analysis may be suitable for an introductory course on quantum mechanics to illustrate the application of the Rayleigh-Ritz variational method to a problem where the boundary conditions play a relevant role and have to be introduced carefully into the trial function. Besides, the examples are suitable for motivating the students to resort to any computer-algebra software in order to calculate the required integrals and solve the secular equations.
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
-
DELTA POTENTIAL
HARMONIC OSCILLATOR
PERTURBATION THEORY
VARIATIONAL METHOD - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/203483
Ver los metadatos del registro completo
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Variational approach to the Schrödinger equation with a delta-function potentialFernández, Francisco MarceloDELTA POTENTIALHARMONIC OSCILLATORPERTURBATION THEORYVARIATIONAL METHODhttps://purl.org/becyt/ford/1.4https://purl.org/becyt/ford/1We obtain accurate eigenvalues of the one-dimensional Schrödinger equation with a Hamiltonian of the form H g = H + gd(x), where d(x) is the Dirac delta function. We show that the well known Rayleigh-Ritz variational method is a suitable approach provided that the basis set takes into account the effect of the Dirac delta on the wavefunction. Present analysis may be suitable for an introductory course on quantum mechanics to illustrate the application of the Rayleigh-Ritz variational method to a problem where the boundary conditions play a relevant role and have to be introduced carefully into the trial function. Besides, the examples are suitable for motivating the students to resort to any computer-algebra software in order to calculate the required integrals and solve the secular equations.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 Publishing2022-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/203483Fernández, Francisco Marcelo; Variational approach to the Schrödinger equation with a delta-function potential; IOP Publishing; European Journal of Physics; 43; 2; 3-2022; 1-7; 0254010143-0807CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1088/1361-6404/ac3f27info:eu-repo/semantics/altIdentifier/url/https://iopscience.iop.org/article/10.1088/1361-6404/ac3f27info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:55:43Zoai:ri.conicet.gov.ar:11336/203483instacron: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:34982025-09-03 09:55:43.824CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Variational approach to the Schrödinger equation with a delta-function potential |
title |
Variational approach to the Schrödinger equation with a delta-function potential |
spellingShingle |
Variational approach to the Schrödinger equation with a delta-function potential Fernández, Francisco Marcelo DELTA POTENTIAL HARMONIC OSCILLATOR PERTURBATION THEORY VARIATIONAL METHOD |
title_short |
Variational approach to the Schrödinger equation with a delta-function potential |
title_full |
Variational approach to the Schrödinger equation with a delta-function potential |
title_fullStr |
Variational approach to the Schrödinger equation with a delta-function potential |
title_full_unstemmed |
Variational approach to the Schrödinger equation with a delta-function potential |
title_sort |
Variational approach to the Schrödinger equation with a delta-function potential |
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 |
DELTA POTENTIAL HARMONIC OSCILLATOR PERTURBATION THEORY VARIATIONAL METHOD |
topic |
DELTA POTENTIAL HARMONIC OSCILLATOR PERTURBATION THEORY VARIATIONAL METHOD |
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 obtain accurate eigenvalues of the one-dimensional Schrödinger equation with a Hamiltonian of the form H g = H + gd(x), where d(x) is the Dirac delta function. We show that the well known Rayleigh-Ritz variational method is a suitable approach provided that the basis set takes into account the effect of the Dirac delta on the wavefunction. Present analysis may be suitable for an introductory course on quantum mechanics to illustrate the application of the Rayleigh-Ritz variational method to a problem where the boundary conditions play a relevant role and have to be introduced carefully into the trial function. Besides, the examples are suitable for motivating the students to resort to any computer-algebra software in order to calculate the required integrals and solve the secular equations. 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 obtain accurate eigenvalues of the one-dimensional Schrödinger equation with a Hamiltonian of the form H g = H + gd(x), where d(x) is the Dirac delta function. We show that the well known Rayleigh-Ritz variational method is a suitable approach provided that the basis set takes into account the effect of the Dirac delta on the wavefunction. Present analysis may be suitable for an introductory course on quantum mechanics to illustrate the application of the Rayleigh-Ritz variational method to a problem where the boundary conditions play a relevant role and have to be introduced carefully into the trial function. Besides, the examples are suitable for motivating the students to resort to any computer-algebra software in order to calculate the required integrals and solve the secular equations. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-03 |
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/11336/203483 Fernández, Francisco Marcelo; Variational approach to the Schrödinger equation with a delta-function potential; IOP Publishing; European Journal of Physics; 43; 2; 3-2022; 1-7; 025401 0143-0807 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/203483 |
identifier_str_mv |
Fernández, Francisco Marcelo; Variational approach to the Schrödinger equation with a delta-function potential; IOP Publishing; European Journal of Physics; 43; 2; 3-2022; 1-7; 025401 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/doi/10.1088/1361-6404/ac3f27 info:eu-repo/semantics/altIdentifier/url/https://iopscience.iop.org/article/10.1088/1361-6404/ac3f27 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by/2.5/ar/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by/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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1842269362579308544 |
score |
13.13397 |