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 |
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| Date: | 2016 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2016
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| 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| _version_ | 1862577444082417664 |
|---|---|
| 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.
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| first_indexed | 2025-11-26T15:27:56Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147848 |
| 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 |
| record_format | dspace |
| 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 |