Symmetry in Nonlinear Mathematical Physics - 2009

Ivan Burban (Bogolyubov Institute for Theoretical Physics, Kyiv, Ukraine)

Generalized five-parameter deformation of one-mode oscillator algebra

We define an generalized (q;α,β,γ;ν)-deformed oscillator algebra and find its structure function of deformation. This algebra includes many other well-known deformations as special cases. We give the classification of irreducible representations of this algebra. We analyze the asymptotic behaviour of the energy levels of this oscillator depending on variation of the deformation parameters. We extract the deformed oscillator with discrete spectrum of its ''quantized coordinate''. We find the eigenvalues of this operator and show that the corresponding eigenfunctions are expressed in terms of the q-deformed (generalized) Hermitian I polynomials.