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

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.

References in corpus (1)

• The q-harmonic oscillator and an analog of the Charlier polynomials

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