Pole structure of the Hamiltonian ζ-function for a singular potential
- Autores
- Falomir, Horacio Alberto; González Pisani, Pablo Andrés; Wipf, Andreas
- Año de publicación
- 2002
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We study the pole structure of the ζ-function associated with the Hamiltonian H of a quantum mechanical particle living in the half-line R⁺, subject to the singular potential gx⁻² + x². We show that H admits nontrivial self-adjoint extensions (SAE) in a given range of values of the parameter g. The ζ-functions of these operators present poles which depend on g and, in general, do not coincide with half an integer (they can even be irrational). The corresponding residues depend on the SAE considered.
Facultad de Ciencias Exactas
Instituto de Física La Plata - Materia
-
Ciencias Exactas
Física
Operator theory
Functional analytical methods
Quantum theory
Ordinary differential operators - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by-nc-sa/4.0/
- Repositorio
.jpg)
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/129682
Ver los metadatos del registro completo
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Pole structure of the Hamiltonian ζ-function for a singular potentialFalomir, Horacio AlbertoGonzález Pisani, Pablo AndrésWipf, AndreasCiencias ExactasFísicaOperator theoryFunctional analytical methodsQuantum theoryOrdinary differential operatorsWe study the pole structure of the ζ-function associated with the Hamiltonian H of a quantum mechanical particle living in the half-line R⁺, subject to the singular potential gx⁻² + x². We show that H admits nontrivial self-adjoint extensions (SAE) in a given range of values of the parameter g. The ζ-functions of these operators present poles which depend on g and, in general, do not coincide with half an integer (they can even be irrational). The corresponding residues depend on the SAE considered.Facultad de Ciencias ExactasInstituto de Física La Plata2002-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf5427-5444http://sedici.unlp.edu.ar/handle/10915/129682enginfo:eu-repo/semantics/altIdentifier/issn/0305-4470info:eu-repo/semantics/altIdentifier/issn/1361-6447info:eu-repo/semantics/altIdentifier/arxiv/math-ph/0112019info:eu-repo/semantics/altIdentifier/doi/10.1088/0305-4470/35/26/306info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:31:13Zoai:sedici.unlp.edu.ar:10915/129682Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:31:13.973SEDICI (UNLP) - Universidad Nacional de La Platafalse |
| dc.title.none.fl_str_mv |
Pole structure of the Hamiltonian ζ-function for a singular potential |
| title |
Pole structure of the Hamiltonian ζ-function for a singular potential |
| spellingShingle |
Pole structure of the Hamiltonian ζ-function for a singular potential Falomir, Horacio Alberto Ciencias Exactas Física Operator theory Functional analytical methods Quantum theory Ordinary differential operators |
| title_short |
Pole structure of the Hamiltonian ζ-function for a singular potential |
| title_full |
Pole structure of the Hamiltonian ζ-function for a singular potential |
| title_fullStr |
Pole structure of the Hamiltonian ζ-function for a singular potential |
| title_full_unstemmed |
Pole structure of the Hamiltonian ζ-function for a singular potential |
| title_sort |
Pole structure of the Hamiltonian ζ-function for a singular potential |
| dc.creator.none.fl_str_mv |
Falomir, Horacio Alberto González Pisani, Pablo Andrés Wipf, Andreas |
| author |
Falomir, Horacio Alberto |
| author_facet |
Falomir, Horacio Alberto González Pisani, Pablo Andrés Wipf, Andreas |
| author_role |
author |
| author2 |
González Pisani, Pablo Andrés Wipf, Andreas |
| author2_role |
author author |
| dc.subject.none.fl_str_mv |
Ciencias Exactas Física Operator theory Functional analytical methods Quantum theory Ordinary differential operators |
| topic |
Ciencias Exactas Física Operator theory Functional analytical methods Quantum theory Ordinary differential operators |
| dc.description.none.fl_txt_mv |
We study the pole structure of the ζ-function associated with the Hamiltonian H of a quantum mechanical particle living in the half-line R⁺, subject to the singular potential gx⁻² + x². We show that H admits nontrivial self-adjoint extensions (SAE) in a given range of values of the parameter g. The ζ-functions of these operators present poles which depend on g and, in general, do not coincide with half an integer (they can even be irrational). The corresponding residues depend on the SAE considered. Facultad de Ciencias Exactas Instituto de Física La Plata |
| description |
We study the pole structure of the ζ-function associated with the Hamiltonian H of a quantum mechanical particle living in the half-line R⁺, subject to the singular potential gx⁻² + x². We show that H admits nontrivial self-adjoint extensions (SAE) in a given range of values of the parameter g. The ζ-functions of these operators present poles which depend on g and, in general, do not coincide with half an integer (they can even be irrational). The corresponding residues depend on the SAE considered. |
| publishDate |
2002 |
| dc.date.none.fl_str_mv |
2002-06 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Articulo http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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article |
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publishedVersion |
| dc.identifier.none.fl_str_mv |
http://sedici.unlp.edu.ar/handle/10915/129682 |
| url |
http://sedici.unlp.edu.ar/handle/10915/129682 |
| dc.language.none.fl_str_mv |
eng |
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eng |
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info:eu-repo/semantics/altIdentifier/issn/0305-4470 info:eu-repo/semantics/altIdentifier/issn/1361-6447 info:eu-repo/semantics/altIdentifier/arxiv/math-ph/0112019 info:eu-repo/semantics/altIdentifier/doi/10.1088/0305-4470/35/26/306 |
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openAccess |
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