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

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

1994-02-03

arxiv.org/abs/hep-th/9402014v1

Phys.Lett. B331 (1994) 150-156

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, Latex file, FTUV/ 93-53, IFIC/ 93-34

Scientific paper

10.1016/0370-2693(94)90956-3

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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