Deformed su(1,1) Algebra as a Model for Quantum Oscillators
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Deformed su(1,1) Algebra as a Model for Quantum Oscillators
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| Creator |
Jafarov, E.I.
Stoilova, N.I. Van der Jeugt, J. |
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| 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.
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| Date |
2019-02-18T12:06:16Z
2019-02-18T12:06:16Z 2012 |
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| Type |
Article
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| Identifier |
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 http://dspace.nbuv.gov.ua/handle/123456789/148417 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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