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

Vadim V. Borzov·Eugene V. Damaskinsky
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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.

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Vadim V. Borzov, Eugene V. Damaskinsky. 2003-08-18. Generalized coherent states for q-oscillator connected with q-Hermite polynomials. https://arxiv.org/abs/math/0307356

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