Quasi-exactly solvable potentials on the line and orthogonal polynomials

In this paper we show that a quasi-exactly solvable (normalizable or periodic) one-dimensional Hamiltonian satisfying very mild conditions defines a family of weakly orthogonal polynomials which obey a three-term recursion relation. in particular, we prove that (normalizable) exactly solvable one-di...

Descripción completa

Detalles Bibliográficos
Autores: Finkel Morgenstern, Federico, González López, Artemio, Rodríguez González, Miguel Ángel
Tipo de recurso: artículo
Fecha de publicación:1996
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/59672
Acceso en línea:https://hdl.handle.net/20.500.14352/59672
Access Level:acceso abierto
Palabra clave:51-73
Física-Modelos matemáticos
Física matemática
id ES_2f221c2c516236ca8a451b770834ca25
oai_identifier_str oai:docta.ucm.es:20.500.14352/59672
network_acronym_str ES
network_name_str España
repository_id_str
spelling Quasi-exactly solvable potentials on the line and orthogonal polynomialsFinkel Morgenstern, FedericoGonzález López, ArtemioRodríguez González, Miguel Ángel51-73Física-Modelos matemáticosFísica matemáticaIn this paper we show that a quasi-exactly solvable (normalizable or periodic) one-dimensional Hamiltonian satisfying very mild conditions defines a family of weakly orthogonal polynomials which obey a three-term recursion relation. in particular, we prove that (normalizable) exactly solvable one-dimensional systems are characterized by the fact that their associated polynomials satisfy a two-term recursion relation. We study the properties of the family of weakly orthogonal polynomials defined by an arbitrary one-dimensional quasi-exactly solvable Hamiltonian, showing in particular that its associated Stieltjes measure is supported on a finite set. From this we deduce that the corresponding moment problem is determined, and that the kth moment grows Like the kth power of a constant as k tends to infinity. We also show that the moments satisfy a constant coefficient linear difference equation, and that this property actually characterizes weakly orthogonal polynomial systems.American Institute of PhysicsUniversidad Complutense de Madrid19961996-08-0119961996-08-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/59672reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/596722026-06-02T12:44:21Z
dc.title.none.fl_str_mv Quasi-exactly solvable potentials on the line and orthogonal polynomials
title Quasi-exactly solvable potentials on the line and orthogonal polynomials
spellingShingle Quasi-exactly solvable potentials on the line and orthogonal polynomials
Finkel Morgenstern, Federico
51-73
Física-Modelos matemáticos
Física matemática
title_short Quasi-exactly solvable potentials on the line and orthogonal polynomials
title_full Quasi-exactly solvable potentials on the line and orthogonal polynomials
title_fullStr Quasi-exactly solvable potentials on the line and orthogonal polynomials
title_full_unstemmed Quasi-exactly solvable potentials on the line and orthogonal polynomials
title_sort Quasi-exactly solvable potentials on the line and orthogonal polynomials
dc.creator.none.fl_str_mv Finkel Morgenstern, Federico
González López, Artemio
Rodríguez González, Miguel Ángel
author Finkel Morgenstern, Federico
author_facet Finkel Morgenstern, Federico
González López, Artemio
Rodríguez González, Miguel Ángel
author_role author
author2 González López, Artemio
Rodríguez González, Miguel Ángel
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 51-73
Física-Modelos matemáticos
Física matemática
topic 51-73
Física-Modelos matemáticos
Física matemática
description In this paper we show that a quasi-exactly solvable (normalizable or periodic) one-dimensional Hamiltonian satisfying very mild conditions defines a family of weakly orthogonal polynomials which obey a three-term recursion relation. in particular, we prove that (normalizable) exactly solvable one-dimensional systems are characterized by the fact that their associated polynomials satisfy a two-term recursion relation. We study the properties of the family of weakly orthogonal polynomials defined by an arbitrary one-dimensional quasi-exactly solvable Hamiltonian, showing in particular that its associated Stieltjes measure is supported on a finite set. From this we deduce that the corresponding moment problem is determined, and that the kth moment grows Like the kth power of a constant as k tends to infinity. We also show that the moments satisfy a constant coefficient linear difference equation, and that this property actually characterizes weakly orthogonal polynomial systems.
publishDate 1996
dc.date.none.fl_str_mv 1996
1996-08-01
1996
1996-08-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/59672
url https://hdl.handle.net/20.500.14352/59672
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv American Institute of Physics
publisher.none.fl_str_mv American Institute of Physics
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869405457621188608
score 15.300719

Similares en LA Referencia