Arik–Coon oscillator with q > 1 in the framework of unified (q; α, β, γ; ν)-deformation

Abstract

In this paper we study the Arik–Coon oscillator with the main relation aa+ − qa+a = 1, where q > 1, in the framework of the unified (q; α, β, γ; ν)-deformed oscillator algebra. This oscillator is connected with the Askey q−1-Hermite polynomials. We construct a family of the generalized coherent states associated with these polynomials and give their explicit expression in terms of standard special functions. By means of the solution of the appropriate classical moment problem, we prove the over-completeness of this family of coherent states.