Deformed su(1,1) Algebra as a Model for Quantum Oscillators
The Lie algebra su(1,1) can be deformed by a reflection operator, in such a way that the positive discrete series representations of su(1,1) can be extended to representations of this deformed algebra su(1,1)γ. Just as the positive discrete series representations of su(1,1) can be used to model a qu...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2012 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2012
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/148417 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Deformed su(1,1) Algebra as a Model for Quantum Oscillators / E.I. Jafarov, N.I. Stoilova, J. Van der Jeugt // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 33 назв. — англ. |
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Jafarov, E.I. Stoilova, N.I. Van der Jeugt, J. 2019-02-18T12:06:16Z 2019-02-18T12:06:16Z 2012 Deformed su(1,1) Algebra as a Model for Quantum Oscillators / E.I. Jafarov, N.I. Stoilova, J. Van der Jeugt // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 33 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81R05; 81Q65; 33C45 DOI: http://dx.doi.org/10.3842/SIGMA.2012.025 https://nasplib.isofts.kiev.ua/handle/123456789/148417 The Lie algebra su(1,1) can be deformed by a reflection operator, in such a way that the positive discrete series representations of su(1,1) can be extended to representations of this deformed algebra su(1,1)γ. Just as the positive discrete series representations of su(1,1) can be used to model a quantum oscillator with Meixner-Pollaczek polynomials as wave functions, the corresponding representations of su(1,1)γ can be utilized to construct models of a quantum oscillator. In this case, the wave functions are expressed in terms of continuous dual Hahn polynomials. We study some properties of these wave functions, and illustrate some features in plots. We also discuss some interesting limits and special cases of the obtained oscillator models. E.I. Jafarov was supported by a postdoc fellowship from the Azerbaijan National Academy of Sciences. N.I. Stoilova was supported by project P6/02 of the Interuniversity Attraction Poles Programme (Belgian State – Belgian Science Policy). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Deformed su(1,1) Algebra as a Model for Quantum Oscillators Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Deformed su(1,1) Algebra as a Model for Quantum Oscillators |
| spellingShingle |
Deformed su(1,1) Algebra as a Model for Quantum Oscillators Jafarov, E.I. Stoilova, N.I. Van der Jeugt, J. |
| title_short |
Deformed su(1,1) Algebra as a Model for Quantum Oscillators |
| title_full |
Deformed su(1,1) Algebra as a Model for Quantum Oscillators |
| title_fullStr |
Deformed su(1,1) Algebra as a Model for Quantum Oscillators |
| title_full_unstemmed |
Deformed su(1,1) Algebra as a Model for Quantum Oscillators |
| title_sort |
deformed su(1,1) algebra as a model for quantum oscillators |
| author |
Jafarov, E.I. Stoilova, N.I. Van der Jeugt, J. |
| author_facet |
Jafarov, E.I. Stoilova, N.I. Van der Jeugt, J. |
| publishDate |
2012 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
The Lie algebra su(1,1) can be deformed by a reflection operator, in such a way that the positive discrete series representations of su(1,1) can be extended to representations of this deformed algebra su(1,1)γ. Just as the positive discrete series representations of su(1,1) can be used to model a quantum oscillator with Meixner-Pollaczek polynomials as wave functions, the corresponding representations of su(1,1)γ can be utilized to construct models of a quantum oscillator. In this case, the wave functions are expressed in terms of continuous dual Hahn polynomials. We study some properties of these wave functions, and illustrate some features in plots. We also discuss some interesting limits and special cases of the obtained oscillator models.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/148417 |
| citation_txt |
Deformed su(1,1) Algebra as a Model for Quantum Oscillators / E.I. Jafarov, N.I. Stoilova, J. Van der Jeugt // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 33 назв. — англ. |
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2025-12-01T15:53:21Z |
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2025-12-01T15:53:21Z |
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