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The Phase Space Model of Nonrelativistic Quantum Mechanics

We focus on several questions arising during the modelling of quantum systems on a phase space. First, we discuss the choice of phase space and its structure. We include an interesting case of discrete phase space. Then, we introduce the respective algebras of functions containing quantum observable...

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Detalles Bibliográficos
Autores principales: Tosiek, Jaromir, Przanowski, Maciej
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8150381/
https://www.ncbi.nlm.nih.gov/pubmed/34066810
http://dx.doi.org/10.3390/e23050581
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author Tosiek, Jaromir
Przanowski, Maciej
author_facet Tosiek, Jaromir
Przanowski, Maciej
author_sort Tosiek, Jaromir
collection PubMed
description We focus on several questions arising during the modelling of quantum systems on a phase space. First, we discuss the choice of phase space and its structure. We include an interesting case of discrete phase space. Then, we introduce the respective algebras of functions containing quantum observables. We also consider the possibility of performing strict calculations and indicate cases where only formal considerations can be performed. We analyse alternative realisations of strict and formal calculi, which are determined by different kernels. Finally, two classes of Wigner functions as representations of states are investigated.
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spelling pubmed-81503812021-05-27 The Phase Space Model of Nonrelativistic Quantum Mechanics Tosiek, Jaromir Przanowski, Maciej Entropy (Basel) Review We focus on several questions arising during the modelling of quantum systems on a phase space. First, we discuss the choice of phase space and its structure. We include an interesting case of discrete phase space. Then, we introduce the respective algebras of functions containing quantum observables. We also consider the possibility of performing strict calculations and indicate cases where only formal considerations can be performed. We analyse alternative realisations of strict and formal calculi, which are determined by different kernels. Finally, two classes of Wigner functions as representations of states are investigated. MDPI 2021-05-08 /pmc/articles/PMC8150381/ /pubmed/34066810 http://dx.doi.org/10.3390/e23050581 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Review
Tosiek, Jaromir
Przanowski, Maciej
The Phase Space Model of Nonrelativistic Quantum Mechanics
title The Phase Space Model of Nonrelativistic Quantum Mechanics
title_full The Phase Space Model of Nonrelativistic Quantum Mechanics
title_fullStr The Phase Space Model of Nonrelativistic Quantum Mechanics
title_full_unstemmed The Phase Space Model of Nonrelativistic Quantum Mechanics
title_short The Phase Space Model of Nonrelativistic Quantum Mechanics
title_sort phase space model of nonrelativistic quantum mechanics
topic Review
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8150381/
https://www.ncbi.nlm.nih.gov/pubmed/34066810
http://dx.doi.org/10.3390/e23050581
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