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arXiv · hep-th/9402014

Discretization of the phase space for a q-deformed harmonic oscillator with q a root of unity

D. Bonatsos·C. Daskaloyannis·D. Ellinas·A. Faessler
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Abstract

The ``position'' and ``momentum'' operators for the q-deformed oscillator with q being a root of unity are proved to have discrete eigenvalues which are roots of deformed Hermite polynomials. The Fourier transform connecting the ``position'' and ``momentum'' representations is also found The phase space of this oscillator has a lattice structure, which is a non-uniformly distributed grid. Non-equidistant lattice structures also occur in the cases of the truncated harmonic oscillator and of the q-deformed parafermionic oscillator, while the parafermionic oscillator corresponds to a uniformly distributed grid.

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D. Bonatsos, C. Daskaloyannis, D. Ellinas, A. Faessler. 1994-02-03. Discretization of the phase space for a q-deformed harmonic oscillator with q a root of unity. https://doi.org/10.1016/0370-2693(94)90956-3

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