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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Дата:2016
Автор: Rastelli, G.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2016
Назва видання:Symmetry, Integrability and Geometry: Methods and Applications
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/147848
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати: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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spelling irk-123456789-1478482019-02-17T01:27:29Z Born-Jordan and Weyl Quantizations of the 2D Anisotropic Harmonic Oscillator Rastelli, G. 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. 2016 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147848 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
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.
format Article
author Rastelli, G.
spellingShingle Rastelli, G.
Born-Jordan and Weyl Quantizations of the 2D Anisotropic Harmonic Oscillator
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Rastelli, G.
author_sort Rastelli, G.
title 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_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_sort born-jordan and weyl quantizations of the 2d anisotropic harmonic oscillator
publisher Інститут математики НАН України
publishDate 2016
url http://dspace.nbuv.gov.ua/handle/123456789/147848
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.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT rastellig bornjordanandweylquantizationsofthe2danisotropicharmonicoscillator
first_indexed 2023-05-20T17:28:40Z
last_indexed 2023-05-20T17:28:40Z
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