  We study the Harmonic and Dirac Oscillator problem extended to a
three-dimensional noncom- mutative space where the noncommutativity is induced
by a shift of the dynamical variables with generators of SL(2;R) in a unitary
irreducible representation. The Hilbert space gets the structure of a direct
product with the representation space as a factor, where there exist operators
which realize the algebra of Lorentz transformations. The spectrum of these
models are considered in perturbation theory, both for small and large
noncommutativity parameters, finding no constraints between coordinates and
momenta noncom- mutativity parameters. Since the representation space of the
unitary irreducible representations SL(2;R) can be realized in terms of spaces
of square-integrable functions, we conclude that these models are equivalent to
quantum mechanical models of particles living in a space with an additional
compact dimension.
  PACS: 03.65.-w; 11.30.Cp; 02.40.Gh
