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.