Wave packet dynamics for a non-linear Schrödinger equation describing continuous position measurements

Autores
Zander, C.; Plastino, Ángel Ricardo; Díaz Alonso, J.
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We investigate time-dependent solutions for a non-linear Schrödinger equation recently proposed by Nassar and Miret-Artés (NM) to describe the continuous measurement of the position of a quantum particle (Nassar, 2013; Nassar and Miret-Artés, 2013). Here we extend these previous studies in two different directions. On the one hand, we incorporate a potential energy term in the NM equation and explore the corresponding wave packet dynamics, while in the previous works the analysis was restricted to the free-particle case. On the other hand, we investigate time-dependent solutions while previous studies focused on a stationary one. We obtain exact wave packet solutions for linear and quadratic potentials, and approximate solutions for the Morse potential. The free-particle case is also revisited from a time-dependent point of view. Our analysis of time-dependent solutions allows us to determine the stability properties of the stationary solution considered in Nassar (2013), Nassar and Miret-Artés (2013). On the basis of these results we reconsider the Bohmian approach to the NM equation, taking into account the fact that the evolution equation for the probability density ρ=|ψ|2 is not a continuity equation. We show that the effect of the source term appearing in the evolution equation for ρ has to be explicitly taken into account when interpreting the NM equation from a Bohmian point of view.
Fil: Zander, C.. University of Pretoria; Sudáfrica
Fil: Plastino, Ángel Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigaciones y Transferencia del Noroeste de la Provincia de Buenos Aires. Universidad Nacional del Noroeste de la Provincia de Buenos Aires. Centro de Investigaciones y Transferencia del Noroeste de la Provincia de Buenos Aires; Argentina
Fil: Díaz Alonso, J.. Université Paris Diderot - Paris 7; Francia. Universidad de Oviedo; España
Materia
NONLINEAR PHYSICS
NONLINEAR SCHRÖDINGER EQUATION
QUANTUM MEASUREMENT
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:11336/85742
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/85742
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Wave packet dynamics for a non-linear Schrödinger equation describing continuous position measurementsZander, C.Plastino, Ángel RicardoDíaz Alonso, J.NONLINEAR PHYSICSNONLINEAR SCHRÖDINGER EQUATIONQUANTUM MEASUREMENThttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We investigate time-dependent solutions for a non-linear Schrödinger equation recently proposed by Nassar and Miret-Artés (NM) to describe the continuous measurement of the position of a quantum particle (Nassar, 2013; Nassar and Miret-Artés, 2013). Here we extend these previous studies in two different directions. On the one hand, we incorporate a potential energy term in the NM equation and explore the corresponding wave packet dynamics, while in the previous works the analysis was restricted to the free-particle case. On the other hand, we investigate time-dependent solutions while previous studies focused on a stationary one. We obtain exact wave packet solutions for linear and quadratic potentials, and approximate solutions for the Morse potential. The free-particle case is also revisited from a time-dependent point of view. Our analysis of time-dependent solutions allows us to determine the stability properties of the stationary solution considered in Nassar (2013), Nassar and Miret-Artés (2013). On the basis of these results we reconsider the Bohmian approach to the NM equation, taking into account the fact that the evolution equation for the probability density ρ=|ψ|2 is not a continuity equation. We show that the effect of the source term appearing in the evolution equation for ρ has to be explicitly taken into account when interpreting the NM equation from a Bohmian point of view.Fil: Zander, C.. University of Pretoria; SudáfricaFil: Plastino, Ángel Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigaciones y Transferencia del Noroeste de la Provincia de Buenos Aires. Universidad Nacional del Noroeste de la Provincia de Buenos Aires. Centro de Investigaciones y Transferencia del Noroeste de la Provincia de Buenos Aires; ArgentinaFil: Díaz Alonso, J.. Université Paris Diderot - Paris 7; Francia. Universidad de Oviedo; EspañaAcademic Press Inc Elsevier Science2015-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/85742Zander, C.; Plastino, Ángel Ricardo; Díaz Alonso, J.; Wave packet dynamics for a non-linear Schrödinger equation describing continuous position measurements; Academic Press Inc Elsevier Science; Annals of Physics (New York); 362; 11-2015; 36-560003-4916CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.aop.2015.07.019info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0003491615002845info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:57:04Zoai:ri.conicet.gov.ar:11336/85742instacron: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 09:57:04.578CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Wave packet dynamics for a non-linear Schrödinger equation describing continuous position measurements
title Wave packet dynamics for a non-linear Schrödinger equation describing continuous position measurements
spellingShingle Wave packet dynamics for a non-linear Schrödinger equation describing continuous position measurements
Zander, C.
NONLINEAR PHYSICS
NONLINEAR SCHRÖDINGER EQUATION
QUANTUM MEASUREMENT
title_short Wave packet dynamics for a non-linear Schrödinger equation describing continuous position measurements
title_full Wave packet dynamics for a non-linear Schrödinger equation describing continuous position measurements
title_fullStr Wave packet dynamics for a non-linear Schrödinger equation describing continuous position measurements
title_full_unstemmed Wave packet dynamics for a non-linear Schrödinger equation describing continuous position measurements
title_sort Wave packet dynamics for a non-linear Schrödinger equation describing continuous position measurements
dc.creator.none.fl_str_mv Zander, C.
Plastino, Ángel Ricardo
Díaz Alonso, J.
author Zander, C.
author_facet Zander, C.
Plastino, Ángel Ricardo
Díaz Alonso, J.
author_role author
author2 Plastino, Ángel Ricardo
Díaz Alonso, J.
author2_role author
author
dc.subject.none.fl_str_mv NONLINEAR PHYSICS
NONLINEAR SCHRÖDINGER EQUATION
QUANTUM MEASUREMENT
topic NONLINEAR PHYSICS
NONLINEAR SCHRÖDINGER EQUATION
QUANTUM MEASUREMENT
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 investigate time-dependent solutions for a non-linear Schrödinger equation recently proposed by Nassar and Miret-Artés (NM) to describe the continuous measurement of the position of a quantum particle (Nassar, 2013; Nassar and Miret-Artés, 2013). Here we extend these previous studies in two different directions. On the one hand, we incorporate a potential energy term in the NM equation and explore the corresponding wave packet dynamics, while in the previous works the analysis was restricted to the free-particle case. On the other hand, we investigate time-dependent solutions while previous studies focused on a stationary one. We obtain exact wave packet solutions for linear and quadratic potentials, and approximate solutions for the Morse potential. The free-particle case is also revisited from a time-dependent point of view. Our analysis of time-dependent solutions allows us to determine the stability properties of the stationary solution considered in Nassar (2013), Nassar and Miret-Artés (2013). On the basis of these results we reconsider the Bohmian approach to the NM equation, taking into account the fact that the evolution equation for the probability density ρ=|ψ|2 is not a continuity equation. We show that the effect of the source term appearing in the evolution equation for ρ has to be explicitly taken into account when interpreting the NM equation from a Bohmian point of view.
Fil: Zander, C.. University of Pretoria; Sudáfrica
Fil: Plastino, Ángel Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigaciones y Transferencia del Noroeste de la Provincia de Buenos Aires. Universidad Nacional del Noroeste de la Provincia de Buenos Aires. Centro de Investigaciones y Transferencia del Noroeste de la Provincia de Buenos Aires; Argentina
Fil: Díaz Alonso, J.. Université Paris Diderot - Paris 7; Francia. Universidad de Oviedo; España
description We investigate time-dependent solutions for a non-linear Schrödinger equation recently proposed by Nassar and Miret-Artés (NM) to describe the continuous measurement of the position of a quantum particle (Nassar, 2013; Nassar and Miret-Artés, 2013). Here we extend these previous studies in two different directions. On the one hand, we incorporate a potential energy term in the NM equation and explore the corresponding wave packet dynamics, while in the previous works the analysis was restricted to the free-particle case. On the other hand, we investigate time-dependent solutions while previous studies focused on a stationary one. We obtain exact wave packet solutions for linear and quadratic potentials, and approximate solutions for the Morse potential. The free-particle case is also revisited from a time-dependent point of view. Our analysis of time-dependent solutions allows us to determine the stability properties of the stationary solution considered in Nassar (2013), Nassar and Miret-Artés (2013). On the basis of these results we reconsider the Bohmian approach to the NM equation, taking into account the fact that the evolution equation for the probability density ρ=|ψ|2 is not a continuity equation. We show that the effect of the source term appearing in the evolution equation for ρ has to be explicitly taken into account when interpreting the NM equation from a Bohmian point of view.
publishDate 2015
dc.date.none.fl_str_mv 2015-11
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/11336/85742
Zander, C.; Plastino, Ángel Ricardo; Díaz Alonso, J.; Wave packet dynamics for a non-linear Schrödinger equation describing continuous position measurements; Academic Press Inc Elsevier Science; Annals of Physics (New York); 362; 11-2015; 36-56
0003-4916
CONICET Digital
CONICET
url http://hdl.handle.net/11336/85742
identifier_str_mv Zander, C.; Plastino, Ángel Ricardo; Díaz Alonso, J.; Wave packet dynamics for a non-linear Schrödinger equation describing continuous position measurements; Academic Press Inc Elsevier Science; Annals of Physics (New York); 362; 11-2015; 36-56
0003-4916
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aop.2015.07.019
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0003491615002845
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 Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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 13.13397

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