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Deformed su (1,1) algebra as a model for quantum oscillators

Elchin Jafarov (UGent) , Nedialka Stoilova (UGent) and Joris Van der Jeugt (UGent)
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Abstract
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 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.
Keywords
Meixner-Pollaczek polynomial, continuous dual Hahn polynomial, oscillator model, deformed algebra su(1_1), FINITE 2-DIMENSIONAL OSCILLATOR, GROUP THEORETIC INTERPRETATIONS, ORTHOGONAL POLYNOMIALS, REPRESENTATIONS, OPERATORS, LIE

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Chicago
Jafarov, Elchin, Nedialka Stoilova, and Joris Van der Jeugt. 2012. “Deformed Su (1,1) Algebra as a Model for Quantum Oscillators.” Symmetry Integrability and Geometry-methods and Applications 8.
APA
Jafarov, Elchin, Stoilova, N., & Van der Jeugt, J. (2012). Deformed su (1,1) algebra as a model for quantum oscillators. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 8.
Vancouver
1.
Jafarov E, Stoilova N, Van der Jeugt J. Deformed su (1,1) algebra as a model for quantum oscillators. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS. 2012;8.
MLA
Jafarov, Elchin, Nedialka Stoilova, and Joris Van der Jeugt. “Deformed Su (1,1) Algebra as a Model for Quantum Oscillators.” SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS 8 (2012): n. pag. Print.
@article{2137364,
  abstract     = {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 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.},
  articleno    = {025},
  author       = {Jafarov, Elchin and Stoilova, Nedialka and Van der Jeugt, Joris},
  issn         = {1815-0659},
  journal      = {SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS},
  keyword      = {Meixner-Pollaczek polynomial,continuous dual Hahn polynomial,oscillator model,deformed algebra su(1\_1),FINITE 2-DIMENSIONAL OSCILLATOR,GROUP THEORETIC INTERPRETATIONS,ORTHOGONAL POLYNOMIALS,REPRESENTATIONS,OPERATORS,LIE},
  language     = {eng},
  pages        = {15},
  title        = {Deformed su (1,1) algebra as a model for quantum oscillators},
  url          = {http://dx.doi.org/10.3842/SIGMA.2012.025},
  volume       = {8},
  year         = {2012},
}

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