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The q-harmonic oscillator and the Al-Salam and Carlitz polynomials

Richard A. Askey·Serge\uı K. Suslov
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Abstract

One more model of a q-harmonic oscillator based on the q-orthogonal polynomials of Al-Salam and Carlitz is discussed. The explicit form of q-creation and q-annihilation operators, q-coherent states and an analog of the Fourier transformation are established. A connection of the kernel of this transform with a family of self-dual biorthogonal rational functions is observed.

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Richard A. Askey, Serge\uı K. Suslov. 1993-07-09. The q-harmonic oscillator and the Al-Salam and Carlitz polynomials. https://doi.org/10.1007/bf00749728

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