Generalized coherent states for $q$-oscillator connected with discrete $q$-Hermite polynomials

V. V. Borzov   ; E. V. Damaskinsky

Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 33, Tome 308 (2004), pp. 48-66

Résumé

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.

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