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

Abstract

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.

Latex2e, 10 pages, Submited to the Proceedings of the international seminar "DAY on DIFFRACTION'2003" v2 Some misprints are corrected

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• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• The integrable multiboson systems and orthogonal polynomials
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Cited by in corpus (1)

• Generalized q-deformed oscillators, q-Hermite polynomials, generalized coherent states