Discretization of the phase space for a q-deformed harmonic oscillator with q a root of unity
High Energy Physics - Theory
2019-08-15 v1
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.
Keywords
Cite
@article{arxiv.hep-th/9402014,
title = {Discretization of the phase space for a q-deformed harmonic oscillator with q a root of unity},
author = {D. Bonatsos and C. Daskaloyannis and D. Ellinas and A. Faessler},
journal= {arXiv preprint arXiv:hep-th/9402014},
year = {2019}
}
Comments
17 pages, Latex file, FTUV/ 93-53, IFIC/ 93-34