Born-Jordan and Weyl Quantizations of the 2D Anisotropic Harmonic Oscillator

We apply the Born-Jordan and Weyl quantization formulas for polynomials in canonical coordinates to the constants of motion of some examples of the superintegrable 2D anisotropic harmonic oscillator. Our aim is to study the behaviour of the algebra of the constants of motion after the different quan...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2016
Main Author: Rastelli, G.
Format: Article
Language:English
Published: Інститут математики НАН України 2016
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/147848
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Born-Jordan and Weyl Quantizations of the 2D Anisotropic Harmonic Oscillator / G. Rastelli // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 15 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Rastelli, G.
author_facet Rastelli, G.
citation_txt Born-Jordan and Weyl Quantizations of the 2D Anisotropic Harmonic Oscillator / G. Rastelli // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 15 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We apply the Born-Jordan and Weyl quantization formulas for polynomials in canonical coordinates to the constants of motion of some examples of the superintegrable 2D anisotropic harmonic oscillator. Our aim is to study the behaviour of the algebra of the constants of motion after the different quantization procedures. In the examples considered, we have that the Weyl formula always preserves the original superintegrable structure of the system, while the Born-Jordan formula, when producing different operators than the Weyl's one, does not.
first_indexed 2025-11-26T15:27:56Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-11-26T15:27:56Z
publishDate 2016
publisher Інститут математики НАН України
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spelling Rastelli, G.
2019-02-16T09:15:55Z
2019-02-16T09:15:55Z
2016
Born-Jordan and Weyl Quantizations of the 2D Anisotropic Harmonic Oscillator / G. Rastelli // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 15 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 81S05; 81R12; 70H06
DOI:10.3842/SIGMA.2016.081
https://nasplib.isofts.kiev.ua/handle/123456789/147848
We apply the Born-Jordan and Weyl quantization formulas for polynomials in canonical coordinates to the constants of motion of some examples of the superintegrable 2D anisotropic harmonic oscillator. Our aim is to study the behaviour of the algebra of the constants of motion after the different quantization procedures. In the examples considered, we have that the Weyl formula always preserves the original superintegrable structure of the system, while the Born-Jordan formula, when producing different operators than the Weyl's one, does not.
I am grateful to the referees of this article for their comments and suggestions.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Born-Jordan and Weyl Quantizations of the 2D Anisotropic Harmonic Oscillator
Article
published earlier
spellingShingle Born-Jordan and Weyl Quantizations of the 2D Anisotropic Harmonic Oscillator
Rastelli, G.
title Born-Jordan and Weyl Quantizations of the 2D Anisotropic Harmonic Oscillator
title_full Born-Jordan and Weyl Quantizations of the 2D Anisotropic Harmonic Oscillator
title_fullStr Born-Jordan and Weyl Quantizations of the 2D Anisotropic Harmonic Oscillator
title_full_unstemmed Born-Jordan and Weyl Quantizations of the 2D Anisotropic Harmonic Oscillator
title_short Born-Jordan and Weyl Quantizations of the 2D Anisotropic Harmonic Oscillator
title_sort born-jordan and weyl quantizations of the 2d anisotropic harmonic oscillator
url https://nasplib.isofts.kiev.ua/handle/123456789/147848
work_keys_str_mv AT rastellig bornjordanandweylquantizationsofthe2danisotropicharmonicoscillator