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Эта публикация цитируется в 9 научных статьях (всего в 9 статьях)
Deformed $\mathfrak{su}(1,1)$ algebra as a model for quantum oscillators
Elchin I. Jafarovab, Neli I. Stoilovac, Joris Van der Jeugtb a Institute of Physics, Azerbaijan National Academy of Sciences, Javid Av. 33, AZ-1143 Baku, Azerbaijan
b Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, B-9000 Gent, Belgium
c Institute for Nuclear Research and Nuclear Energy, Boul. Tsarigradsko Chaussee 72, 1784 Sofia, Bulgaria
Аннотация:
The Lie algebra $\mathfrak{su}(1,1)$ can be deformed by a reflection operator, in such a way that the positive discrete series representations of $\mathfrak{su}(1,1)$ can be extended to representations of this deformed algebra $\mathfrak{su}(1,1)_\gamma$. Just as the positive discrete series representations of $\mathfrak{su}(1,1)$ can be used to model a quantum oscillator with Meixner–Pollaczek polynomials as wave functions,
the corresponding representations of $\mathfrak{su}(1,1)_\gamma$ 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.
Ключевые слова:
oscillator model, deformed algebra $\mathfrak{su}(1,1)$, Meixner–Pollaczek polynomial, continuous dual Hahn polynomial.
Поступила: 17 февраля 2012 г.; в окончательном варианте 8 мая 2012 г.; опубликована 11 мая 2012 г.
Образец цитирования:
Elchin I. Jafarov, Neli I. Stoilova, Joris Van der Jeugt, “Deformed $\mathfrak{su}(1,1)$ algebra as a model for quantum oscillators”, SIGMA, 8 (2012), 025, 15 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma702 https://www.mathnet.ru/rus/sigma/v8/p25
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