For oscillator-like systems, connected with the Laguerre, Legendre and Chebyshev polynomials, coherent states of Glauber-Barut-Girardello type are defined. The suggested construction can be applied to each system of orthogonal polynomials including classical ones as well as deformed ones.
We are continuing here the study of generalized coherent states of Barut-Girardello type for the oscillator-like systems connected with the given set of orthogonal polynomials. In this work we construct the family of coherent states associated with discrete q-Hermite polynomials of the II-type and prove the over-completeness of this family of states by constructing the measure for unity decomposition for this family of coherent states.
We extend our approach to constmction of coherent states for oscillator-like systems connected with given system of orthogonal polynomials to the case of the classical orthogonal polynomials of a discrete variable. In this paper we consider oscillntmor-liksey stem associated with the Meixnct polynomials and compare associated Hamiltonian with the Hamiltonian of the relativistic linear oscillator obtained by the other point of view. We also construct generalized coherent states both Rarut-Girardello and Perelomov types €or this system.
We define the coherent states for the oscillator-like systems, connected with the Chebyshev polynomials Tn(x) and Un(x) of the 1-st and 2-nd kind.