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Journal of Mathematical Sciences

Generalized Coherent States for the q-Oscillator Associated with Discrete q-Hermite Polynomials

Вадим Васильевич Борзов, Eugeniy Viktorovich Damaskinsky

Published Nov 16, 2005• 12 citations
Publisher
DOI
10.1007/s10958-005-0472-9

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

Вадим Васильевич Борзов

For the oscillator-like systems, connected with q-Hermite polynomials, coherent states of Barut-Girardello type are defined. The well-known Arik-Coon oscillator naturally arose in the framework of suggested approach as oscillator, connected with the Rogers q-Hermite polynomials, in the same way as usual oscillator with standard Hermite polynomials. The results about the coherent states for discrete q-Hermite polynomials of II type are quite new.

arXiv:math/0307356•Days on Diffraction•Jan 1, 2003•12 citations
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 qqq-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.