Discretization of the phase space for a q-deformed harmonic oscillator with q a root of unity
نویسندگان
چکیده
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. Permanent address: Institute of Nuclear Physics, N.C.S.R. “Demokritos”, GR-15310 Aghia Paraskevi, Attiki, Greece
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