Discretization of the phase space for a q-deformed harmonic oscillator with q a root of unityDiscretization of the phase space for a q-deformed harmonic oscillator with q a root of unity Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2015-11-091994enThe “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.http://creativecommons.org/licenses/by/4.0/Physics Letters B3311-2150-156 Bonatsos, Dennis Daskaloyannis C. Ellinas Dimosthenis Ελληνας Δημοσθενης Faessler, Amand Elsevier q-deformed oscillator