The Phase Space Model of Nonrelativistic Quantum Mechanics

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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Main Authors: Jaromir Tosiek, Maciej Przanowski
Format: Article
Language:English
Published: MDPI AG 2021-05-01
Series:Entropy
Subjects:
phase space quantum mechanics
Wigner function
discrete phase space
Online Access:https://www.mdpi.com/1099-4300/23/5/581
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spelling doaj-85b3462e281947218f14328c11fe7bd12021-05-31T23:28:49ZengMDPI AGEntropy1099-43002021-05-012358158110.3390/e23050581The Phase Space Model of Nonrelativistic Quantum MechanicsJaromir Tosiek0Maciej Przanowski1Institute of Physics, Łódź University of Technology, 90-924 Łódź, PolandInstitute of Physics, Łódź University of Technology, 90-924 Łódź, PolandWe 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.https://www.mdpi.com/1099-4300/23/5/581phase space quantum mechanicsWigner functiondiscrete phase space
collection DOAJ
language English
format Article
sources DOAJ
author Jaromir Tosiek
Maciej Przanowski
spellingShingle Jaromir Tosiek
Maciej Przanowski
The Phase Space Model of Nonrelativistic Quantum Mechanics
Entropy
phase space quantum mechanics
Wigner function
discrete phase space
author_facet Jaromir Tosiek
Maciej Przanowski
author_sort Jaromir Tosiek
title The Phase Space Model of Nonrelativistic Quantum Mechanics
title_short 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_sort phase space model of nonrelativistic quantum mechanics
publisher MDPI AG
series Entropy
issn 1099-4300
publishDate 2021-05-01
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.
topic phase space quantum mechanics
Wigner function
discrete phase space
url https://www.mdpi.com/1099-4300/23/5/581
work_keys_str_mv AT jaromirtosiek thephasespacemodelofnonrelativisticquantummechanics
AT maciejprzanowski thephasespacemodelofnonrelativisticquantummechanics
AT jaromirtosiek phasespacemodelofnonrelativisticquantummechanics
AT maciejprzanowski phasespacemodelofnonrelativisticquantummechanics
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