Mathematical properties of generalized Sturmian functions

Autores
Ambrosio, Marcelo José; del Punta, Jessica Adriana; Rodriguez, Karina Viviana; Gasaneo, Gustavo; Ancarani, L. U.
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study some mathematical properties of generalized Sturmian functions which are solutions of a Schrödinger-like equation supplemented by two boundary conditions. These generalized functions, for any value of the energy, are defined in terms of the magnitude of the potential. One of the boundary conditions is imposed at the origin of the coordinate, where regularity is required. The second point is at large distances. For negative energies, bound-like conditions are imposed. For positive or complex energies, incoming or outgoing boundary conditions are imposed to deal with scattering problems; in this case, since scattering conditions are complex, the Sturmian functions themselves are complex. Since all of the functions solve a SturmLiouville problem, they allow us to construct a Sturmian basis set which must be orthogonal and complete: this is the case even when they are complex. Here we study some properties of generalized Sturmian functions associated with the Hulthén potential, in particular, the spatial organization of their nodes, and demonstrate explicitly their orthogonality. We also show that the overlap matrix elements, which are generally required in scattering or bound state calculations, are well defined. Many of these mathematical properties are expressed in terms of uncommon multivariable hypergeometric functions. Finally, applications to the scattering of a particle by a Yukawa and by a Hulthén potential serve as illustrations of the efficiency of the complex HulthénSturmian basis.
Fil: Ambrosio, Marcelo José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina
Fil: del Punta, Jessica Adriana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina
Fil: Rodriguez, Karina Viviana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina
Fil: Gasaneo, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina
Fil: Ancarani, L. U.. Université Paul Verlaine-Metz; Francia
Materia
Sturmian Functions
Scattering Problem
Green Operator
Atomic Collisionsions
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:11336/66531
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/66531
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network_name_str CONICET Digital (CONICET)
spelling Mathematical properties of generalized Sturmian functionsAmbrosio, Marcelo Josédel Punta, Jessica AdrianaRodriguez, Karina VivianaGasaneo, GustavoAncarani, L. U.Sturmian FunctionsScattering ProblemGreen OperatorAtomic Collisionsionshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We study some mathematical properties of generalized Sturmian functions which are solutions of a Schrödinger-like equation supplemented by two boundary conditions. These generalized functions, for any value of the energy, are defined in terms of the magnitude of the potential. One of the boundary conditions is imposed at the origin of the coordinate, where regularity is required. The second point is at large distances. For negative energies, bound-like conditions are imposed. For positive or complex energies, incoming or outgoing boundary conditions are imposed to deal with scattering problems; in this case, since scattering conditions are complex, the Sturmian functions themselves are complex. Since all of the functions solve a SturmLiouville problem, they allow us to construct a Sturmian basis set which must be orthogonal and complete: this is the case even when they are complex. Here we study some properties of generalized Sturmian functions associated with the Hulthén potential, in particular, the spatial organization of their nodes, and demonstrate explicitly their orthogonality. We also show that the overlap matrix elements, which are generally required in scattering or bound state calculations, are well defined. Many of these mathematical properties are expressed in terms of uncommon multivariable hypergeometric functions. Finally, applications to the scattering of a particle by a Yukawa and by a Hulthén potential serve as illustrations of the efficiency of the complex HulthénSturmian basis.Fil: Ambrosio, Marcelo José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; ArgentinaFil: del Punta, Jessica Adriana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; ArgentinaFil: Rodriguez, Karina Viviana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; ArgentinaFil: Gasaneo, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; ArgentinaFil: Ancarani, L. U.. Université Paul Verlaine-Metz; FranciaIOP Publishing2012-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/66531Ambrosio, Marcelo José; del Punta, Jessica Adriana; Rodriguez, Karina Viviana; Gasaneo, Gustavo; Ancarani, L. U.; Mathematical properties of generalized Sturmian functions; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 45; 1; 1-2012; 2-211751-81131050-2947CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8113/45/1/015201info:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/article/10.1088/1751-8113/45/1/015201info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:06:55Zoai:ri.conicet.gov.ar:11336/66531instacron: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:34982025-09-10 13:06:55.255CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Mathematical properties of generalized Sturmian functions
title Mathematical properties of generalized Sturmian functions
spellingShingle Mathematical properties of generalized Sturmian functions
Ambrosio, Marcelo José
Sturmian Functions
Scattering Problem
Green Operator
Atomic Collisionsions
title_short Mathematical properties of generalized Sturmian functions
title_full Mathematical properties of generalized Sturmian functions
title_fullStr Mathematical properties of generalized Sturmian functions
title_full_unstemmed Mathematical properties of generalized Sturmian functions
title_sort Mathematical properties of generalized Sturmian functions
dc.creator.none.fl_str_mv Ambrosio, Marcelo José
del Punta, Jessica Adriana
Rodriguez, Karina Viviana
Gasaneo, Gustavo
Ancarani, L. U.
author Ambrosio, Marcelo José
author_facet Ambrosio, Marcelo José
del Punta, Jessica Adriana
Rodriguez, Karina Viviana
Gasaneo, Gustavo
Ancarani, L. U.
author_role author
author2 del Punta, Jessica Adriana
Rodriguez, Karina Viviana
Gasaneo, Gustavo
Ancarani, L. U.
author2_role author
author
author
author
dc.subject.none.fl_str_mv Sturmian Functions
Scattering Problem
Green Operator
Atomic Collisionsions
topic Sturmian Functions
Scattering Problem
Green Operator
Atomic Collisionsions
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study some mathematical properties of generalized Sturmian functions which are solutions of a Schrödinger-like equation supplemented by two boundary conditions. These generalized functions, for any value of the energy, are defined in terms of the magnitude of the potential. One of the boundary conditions is imposed at the origin of the coordinate, where regularity is required. The second point is at large distances. For negative energies, bound-like conditions are imposed. For positive or complex energies, incoming or outgoing boundary conditions are imposed to deal with scattering problems; in this case, since scattering conditions are complex, the Sturmian functions themselves are complex. Since all of the functions solve a SturmLiouville problem, they allow us to construct a Sturmian basis set which must be orthogonal and complete: this is the case even when they are complex. Here we study some properties of generalized Sturmian functions associated with the Hulthén potential, in particular, the spatial organization of their nodes, and demonstrate explicitly their orthogonality. We also show that the overlap matrix elements, which are generally required in scattering or bound state calculations, are well defined. Many of these mathematical properties are expressed in terms of uncommon multivariable hypergeometric functions. Finally, applications to the scattering of a particle by a Yukawa and by a Hulthén potential serve as illustrations of the efficiency of the complex HulthénSturmian basis.
Fil: Ambrosio, Marcelo José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina
Fil: del Punta, Jessica Adriana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina
Fil: Rodriguez, Karina Viviana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina
Fil: Gasaneo, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina
Fil: Ancarani, L. U.. Université Paul Verlaine-Metz; Francia
description We study some mathematical properties of generalized Sturmian functions which are solutions of a Schrödinger-like equation supplemented by two boundary conditions. These generalized functions, for any value of the energy, are defined in terms of the magnitude of the potential. One of the boundary conditions is imposed at the origin of the coordinate, where regularity is required. The second point is at large distances. For negative energies, bound-like conditions are imposed. For positive or complex energies, incoming or outgoing boundary conditions are imposed to deal with scattering problems; in this case, since scattering conditions are complex, the Sturmian functions themselves are complex. Since all of the functions solve a SturmLiouville problem, they allow us to construct a Sturmian basis set which must be orthogonal and complete: this is the case even when they are complex. Here we study some properties of generalized Sturmian functions associated with the Hulthén potential, in particular, the spatial organization of their nodes, and demonstrate explicitly their orthogonality. We also show that the overlap matrix elements, which are generally required in scattering or bound state calculations, are well defined. Many of these mathematical properties are expressed in terms of uncommon multivariable hypergeometric functions. Finally, applications to the scattering of a particle by a Yukawa and by a Hulthén potential serve as illustrations of the efficiency of the complex HulthénSturmian basis.
publishDate 2012
dc.date.none.fl_str_mv 2012-01
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/11336/66531
Ambrosio, Marcelo José; del Punta, Jessica Adriana; Rodriguez, Karina Viviana; Gasaneo, Gustavo; Ancarani, L. U.; Mathematical properties of generalized Sturmian functions; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 45; 1; 1-2012; 2-21
1751-8113
1050-2947
CONICET Digital
CONICET
url http://hdl.handle.net/11336/66531
identifier_str_mv Ambrosio, Marcelo José; del Punta, Jessica Adriana; Rodriguez, Karina Viviana; Gasaneo, Gustavo; Ancarani, L. U.; Mathematical properties of generalized Sturmian functions; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 45; 1; 1-2012; 2-21
1751-8113
1050-2947
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8113/45/1/015201
info:eu-repo/semantics/altIdentifier/url/http://iopscience.iop.org/article/10.1088/1751-8113/45/1/015201
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 12.993085

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