Ad hoc physical Hilbert spaces in Quantum Mechanics

Autores
Fernández, Francisco Marcelo; Garcia, Javier; Semorádová, Iveta; Znojil, Miloslav
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The overall principles of what is now widely known as PT-symmetric quantum mechanics are listed, explained and illustrated via a few examples. In particular, models based on an elementary local interaction V(x) are discussed as motivated by the naturally emergent possibility of an efficient regularization of an otherwise unacceptable presence of a strongly singular repulsive core in the origin. The emphasis is put on the constructive aspects of the models. Besides the overall outline of the formalism we show how the low-lying energies of bound states may be found in closed form in certain dynamical regimes. Finally, once these energies are found real we explain that in spite of a manifest non-Hermiticity of the Hamiltonian the time-evolution of the system becomes unitary in a properly amended physical Hilbert space.
Fil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina. Universidad Nacional de La Plata; Argentina
Fil: Garcia, Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina. Universidad Nacional de La Plata; Argentina
Fil: Semorádová, Iveta. Nuclear Physics Institute ASCR; República Checa
Fil: Znojil, Miloslav. Nuclear Physics Institute ASCR; República Checa
Materia
Pt Symmetry
Singular Interaction
Regularization
Perturbation Theory
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:11336/5154
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Ad hoc physical Hilbert spaces in Quantum MechanicsFernández, Francisco MarceloGarcia, JavierSemorádová, IvetaZnojil, MiloslavPt SymmetrySingular InteractionRegularizationPerturbation Theoryhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The overall principles of what is now widely known as PT-symmetric quantum mechanics are listed, explained and illustrated via a few examples. In particular, models based on an elementary local interaction V(x) are discussed as motivated by the naturally emergent possibility of an efficient regularization of an otherwise unacceptable presence of a strongly singular repulsive core in the origin. The emphasis is put on the constructive aspects of the models. Besides the overall outline of the formalism we show how the low-lying energies of bound states may be found in closed form in certain dynamical regimes. Finally, once these energies are found real we explain that in spite of a manifest non-Hermiticity of the Hamiltonian the time-evolution of the system becomes unitary in a properly amended physical Hilbert space.Fil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina. Universidad Nacional de La Plata; ArgentinaFil: Garcia, Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina. Universidad Nacional de La Plata; ArgentinaFil: Semorádová, Iveta. Nuclear Physics Institute ASCR; República ChecaFil: Znojil, Miloslav. Nuclear Physics Institute ASCR; República ChecaSpringer2014-10-21info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/5154Fernández, Francisco Marcelo; Garcia, Javier; Semorádová, Iveta ; Znojil, Miloslav ; Ad hoc physical Hilbert spaces in Quantum Mechanics; Springer; International Journal Of Theoretical Physics; 54; 12; 21-10-2014; 4187-42030020-7748enginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs10773-014-2376-2info:eu-repo/semantics/altIdentifier/url/http://arxiv.org/abs/1405.7284info:eu-repo/semantics/altIdentifier/doi/10.1007/s10773-014-2376-2info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:07:25Zoai:ri.conicet.gov.ar:11336/5154instacron: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:34982025-09-29 10:07:25.752CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Ad hoc physical Hilbert spaces in Quantum Mechanics
title Ad hoc physical Hilbert spaces in Quantum Mechanics
spellingShingle Ad hoc physical Hilbert spaces in Quantum Mechanics
Fernández, Francisco Marcelo
Pt Symmetry
Singular Interaction
Regularization
Perturbation Theory
title_short Ad hoc physical Hilbert spaces in Quantum Mechanics
title_full Ad hoc physical Hilbert spaces in Quantum Mechanics
title_fullStr Ad hoc physical Hilbert spaces in Quantum Mechanics
title_full_unstemmed Ad hoc physical Hilbert spaces in Quantum Mechanics
title_sort Ad hoc physical Hilbert spaces in Quantum Mechanics
dc.creator.none.fl_str_mv Fernández, Francisco Marcelo
Garcia, Javier
Semorádová, Iveta
Znojil, Miloslav
author Fernández, Francisco Marcelo
author_facet Fernández, Francisco Marcelo
Garcia, Javier
Semorádová, Iveta
Znojil, Miloslav
author_role author
author2 Garcia, Javier
Semorádová, Iveta
Znojil, Miloslav
author2_role author
author
author
dc.subject.none.fl_str_mv Pt Symmetry
Singular Interaction
Regularization
Perturbation Theory
topic Pt Symmetry
Singular Interaction
Regularization
Perturbation Theory
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The overall principles of what is now widely known as PT-symmetric quantum mechanics are listed, explained and illustrated via a few examples. In particular, models based on an elementary local interaction V(x) are discussed as motivated by the naturally emergent possibility of an efficient regularization of an otherwise unacceptable presence of a strongly singular repulsive core in the origin. The emphasis is put on the constructive aspects of the models. Besides the overall outline of the formalism we show how the low-lying energies of bound states may be found in closed form in certain dynamical regimes. Finally, once these energies are found real we explain that in spite of a manifest non-Hermiticity of the Hamiltonian the time-evolution of the system becomes unitary in a properly amended physical Hilbert space.
Fil: Fernández, Francisco Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina. Universidad Nacional de La Plata; Argentina
Fil: Garcia, Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina. Universidad Nacional de La Plata; Argentina
Fil: Semorádová, Iveta. Nuclear Physics Institute ASCR; República Checa
Fil: Znojil, Miloslav. Nuclear Physics Institute ASCR; República Checa
description The overall principles of what is now widely known as PT-symmetric quantum mechanics are listed, explained and illustrated via a few examples. In particular, models based on an elementary local interaction V(x) are discussed as motivated by the naturally emergent possibility of an efficient regularization of an otherwise unacceptable presence of a strongly singular repulsive core in the origin. The emphasis is put on the constructive aspects of the models. Besides the overall outline of the formalism we show how the low-lying energies of bound states may be found in closed form in certain dynamical regimes. Finally, once these energies are found real we explain that in spite of a manifest non-Hermiticity of the Hamiltonian the time-evolution of the system becomes unitary in a properly amended physical Hilbert space.
publishDate 2014
dc.date.none.fl_str_mv 2014-10-21
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/11336/5154
Fernández, Francisco Marcelo; Garcia, Javier; Semorádová, Iveta ; Znojil, Miloslav ; Ad hoc physical Hilbert spaces in Quantum Mechanics; Springer; International Journal Of Theoretical Physics; 54; 12; 21-10-2014; 4187-4203
0020-7748
url http://hdl.handle.net/11336/5154
identifier_str_mv Fernández, Francisco Marcelo; Garcia, Javier; Semorádová, Iveta ; Znojil, Miloslav ; Ad hoc physical Hilbert spaces in Quantum Mechanics; Springer; International Journal Of Theoretical Physics; 54; 12; 21-10-2014; 4187-4203
0020-7748
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007%2Fs10773-014-2376-2
info:eu-repo/semantics/altIdentifier/url/http://arxiv.org/abs/1405.7284
info:eu-repo/semantics/altIdentifier/doi/10.1007/s10773-014-2376-2
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
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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 13.070432

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