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

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

1993-07-09

arxiv.org/abs/math/9307206v1

Mathematics

Classical Analysis and ODEs

Scientific paper

10.1088/0305-4470/26/15/014

A model of a q-harmonic oscillator based on q-Charlier polynomials of
Al-Salam and Carlitz is discussed. Simple explicit realization of q-creation
and q-annihilation operators, q-coherent states and an analog of the Fourier
transformation are found. A connection of the kernel of this transform with
biorthogonal rational functions is observed.

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