The q-harmonic oscillator and an analog of the Charlier polynomials
Classical Analysis and ODEs
2009-10-22 v1 Quantum Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.math/9307206,
title = {The q-harmonic oscillator and an analog of the Charlier polynomials},
author = {Richard A. Askey and Serge\uı K. Suslov},
journal= {arXiv preprint arXiv:math/9307206},
year = {2009}
}