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

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

2012-02-16

arxiv.org/abs/1202.3541v1

Physics

Mathematical Physics

Scientific paper

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.

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