This article is cited in 2 papers

Weyl shift of $q$-oscillator and $q$-polynomials

A. S. Zhedanov

Donetsk Physical-Technical Institute, National Academy of Sciences of Ukraine

Abstract: A unitary Weyl operator $U_q(w)$ that realizes a "$q$-shift" automorphism for the $q$-oscillator is found. Explicit expressions for the matrix elements and coherent states are found. It is shown that the Weyl $q$-operator generates isospectral families of orthogonal polynomials that generalize the Charlier and Hermite polynomials.

Received: 27.04.1992

 English version: Theoretical and Mathematical Physics, 1993, 94:2, 219–224

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