1202.3541 (E. I. Jafarov et al.)

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

E. I. Jafarov, N. I. Stoilova, J. Van der Jeugt

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.

View original: http://arxiv.org/abs/1202.3541