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)_gamma. Just as the positive discrete series representations of su(1,1) can be used to mode...
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2012-05-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2012.025 |
| _version_ | 1818061872224534528 |
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| author | Elchin I. Jafarov Neli I. Stoilova Joris Van der Jeugt |
| author_facet | Elchin I. Jafarov Neli I. Stoilova Joris Van der Jeugt |
| author_sort | Elchin I. Jafarov |
| collection | DOAJ |
| 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)_gamma. 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)_gamma can be utilized to constructmodels 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. |
| first_indexed | 2024-12-10T13:55:13Z |
| format | Article |
| id | doaj.art-6cf9f6fd56cb4044821f3724895ca0b6 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-10T13:55:13Z |
| publishDate | 2012-05-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-6cf9f6fd56cb4044821f3724895ca0b62022-12-22T01:46:01ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592012-05-018025Deformed su(1,1) Algebra as a Model for Quantum OscillatorsElchin I. JafarovNeli I. StoilovaJoris Van der JeugtThe 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)_gamma. 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)_gamma can be utilized to constructmodels 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.http://dx.doi.org/10.3842/SIGMA.2012.025oscillator modeldeformed algebra su(11)Meixner-Pollaczek polynomialcontinuous dual Hahn polynomial |
| spellingShingle | Elchin I. Jafarov Neli I. Stoilova Joris Van der Jeugt Deformed su(1,1) Algebra as a Model for Quantum Oscillators Symmetry, Integrability and Geometry: Methods and Applications oscillator model deformed algebra su(1 1) Meixner-Pollaczek polynomial continuous dual Hahn polynomial |
| title | 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_short | Deformed su(1,1) Algebra as a Model for Quantum Oscillators |
| title_sort | deformed su 1 1 algebra as a model for quantum oscillators |
| topic | oscillator model deformed algebra su(1 1) Meixner-Pollaczek polynomial continuous dual Hahn polynomial |
| url | http://dx.doi.org/10.3842/SIGMA.2012.025 |
| work_keys_str_mv | AT elchinijafarov deformedsu11algebraasamodelforquantumoscillators AT neliistoilova deformedsu11algebraasamodelforquantumoscillators AT jorisvanderjeugt deformedsu11algebraasamodelforquantumoscillators |