Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic Systems

The D-dimensional harmonic system (i.e., a particle moving under the action of a quadratic potential) is, together with the hydrogenic system, the main prototype of the physics of multidimensional quantum systems. In this work, we rigorously determine the leading term of the Heisenberg-like and entr...

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Authors: Puertas-Centeno, D., Toranzo, I. V., Dehesa, J. S.
Format: article
Publication Date:2017
Country:España
Institution:Universidad Rey Juan Carlos
Repository:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
OAI Identifier:oai:burjcdigital.urjc.es:10115/40181
Online Access:https://hdl.handle.net/10115/40181
Access Level:Open access
Keyword:Entropic uncertainty measures
D-dimensional harmonic oscillator
D-dimensional quantum physics
Radial and momentum expectation values
Harmonic states at large dimensions
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spelling Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic SystemsPuertas-Centeno, D.Toranzo, I. V.Dehesa, J. S.Entropic uncertainty measuresD-dimensional harmonic oscillatorD-dimensional quantum physicsRadial and momentum expectation valuesHarmonic states at large dimensionsThe D-dimensional harmonic system (i.e., a particle moving under the action of a quadratic potential) is, together with the hydrogenic system, the main prototype of the physics of multidimensional quantum systems. In this work, we rigorously determine the leading term of the Heisenberg-like and entropy-like uncertainty measures of this system as given by the radial expectation values and the Rényi entropies, respectively, at the limit of large D. The associated multidimensional position-momentum uncertainty relations are discussed, showing that they saturate the corresponding general ones. A conjecture about the Shannon-like uncertainty relation is given, and an interesting phenomenon is observed: the Heisenberg-like and Rényi-entropy-based equality-type uncertainty relations for all of the D-dimensional harmonic oscillator states in the pseudoclassical (D → ∞) limit are the same as the corresponding ones for the hydrogenic systems, despite the so different character of the oscillator and Coulomb potentials.MDPI202420242017info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10115/40181reponame:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlosinstname:Universidad Rey Juan CarlosInglésAttribution 4.0 Internationalhttps://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:burjcdigital.urjc.es:10115/401812026-06-24T12:48:17Z
dc.title.none.fl_str_mv Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic Systems
title Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic Systems
spellingShingle Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic Systems
Puertas-Centeno, D.
Entropic uncertainty measures
D-dimensional harmonic oscillator
D-dimensional quantum physics
Radial and momentum expectation values
Harmonic states at large dimensions
title_short Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic Systems
title_full Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic Systems
title_fullStr Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic Systems
title_full_unstemmed Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic Systems
title_sort Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic Systems
dc.creator.none.fl_str_mv Puertas-Centeno, D.
Toranzo, I. V.
Dehesa, J. S.
author Puertas-Centeno, D.
author_facet Puertas-Centeno, D.
Toranzo, I. V.
Dehesa, J. S.
author_role author
author2 Toranzo, I. V.
Dehesa, J. S.
author2_role author
author
dc.subject.none.fl_str_mv Entropic uncertainty measures
D-dimensional harmonic oscillator
D-dimensional quantum physics
Radial and momentum expectation values
Harmonic states at large dimensions
topic Entropic uncertainty measures
D-dimensional harmonic oscillator
D-dimensional quantum physics
Radial and momentum expectation values
Harmonic states at large dimensions
description The D-dimensional harmonic system (i.e., a particle moving under the action of a quadratic potential) is, together with the hydrogenic system, the main prototype of the physics of multidimensional quantum systems. In this work, we rigorously determine the leading term of the Heisenberg-like and entropy-like uncertainty measures of this system as given by the radial expectation values and the Rényi entropies, respectively, at the limit of large D. The associated multidimensional position-momentum uncertainty relations are discussed, showing that they saturate the corresponding general ones. A conjecture about the Shannon-like uncertainty relation is given, and an interesting phenomenon is observed: the Heisenberg-like and Rényi-entropy-based equality-type uncertainty relations for all of the D-dimensional harmonic oscillator states in the pseudoclassical (D → ∞) limit are the same as the corresponding ones for the hydrogenic systems, despite the so different character of the oscillator and Coulomb potentials.
publishDate 2017
dc.date.none.fl_str_mv 2017
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10115/40181
url https://hdl.handle.net/10115/40181
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv Attribution 4.0 International
https://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution 4.0 International
https://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv reponame:BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
instname:Universidad Rey Juan Carlos
instname_str Universidad Rey Juan Carlos
reponame_str BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
collection BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,198674

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