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 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
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| 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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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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 |
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2023-05-20T17:28:40Z |
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2023-05-20T17:28:40Z |
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1796153386034266112 |