  We investigate a quantum mechanical harmonic oscillator based on the extended
Snyder model. This realization of the Snyder model is constructed as a quantum
phase space generated by $D$ spatial coordinates and $D(D-1)/2$ tensorial
degrees of freedom, together with their conjugate momenta. The \coo obey
nontrivial \cor and generate a noncommutative geometry, which admits nicer
properties than the usual realization of the model, in particular giving rise
to an associative star product.
  The spectrum of the harmonic oscillator is studied through the introduction
of creation and annihilation operators. Some physical consequences of the
introduction of the additional degrees of freedom are discussed.
