Distributed Gaussian polynomials as q-oscillator eigenfunctions

Details Distributed Gaussian polynomials as q-oscillator eigenfunctions Distributed Gaussian polynomials as q-oscillator eigenfunctions

2007-04-24

arxiv.org/abs/0704.3196v1

Journal of Mathematical Physics 47, 013508 (2006)

Physics

Mathematical Physics

Scientific paper

10.1063/1.2161022

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.

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