Distributed Gaussian polynomials as q-oscillator eigenfunctions


Creative Commons License

Karabulut H.

JOURNAL OF MATHEMATICAL PHYSICS, vol.47, no.1, 2006 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 1
  • Publication Date: 2006
  • Doi Number: 10.1063/1.2161022
  • Title of Journal : JOURNAL OF MATHEMATICAL PHYSICS

Abstract

Karabulut and Sibert [J. Math. Phys. 38, 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. (c) 2006 American Institute of Physics.