Distributed Gaussian polynomials as q-oscillator eigenfunctions
Mathematical Physics
2007-05-23 v1 math.MP
Abstract
Karabulut and Sibert (\textit{J. Math. Phys}. \textbf{38} (9), 4815 (1997)) have constructed an orthogonal set of functions from linear combinations of equally spaced Gaussians. In this paper we show that they are actually eigenfunctions of a q-oscillator in coordinate representation. We also reinterpret the coordinate representation example of q-oscillator given by Macfarlane as the functions orthogonal with respect to an unusual inner product definition. It is shown that the eigenfunctions in both q-oscillator examples are infinitely degenerate.
Cite
@article{arxiv.0704.3196,
title = {Distributed Gaussian polynomials as q-oscillator eigenfunctions},
author = {Hasan Karabulut},
journal= {arXiv preprint arXiv:0704.3196},
year = {2007}
}