  We propose an approach based on a generalized quantum mechanics to deal with
the basic features of the intrinsic spin Hall effect. This can be done by
considering two decoupled harmonic oscillators on the noncommutative plane and
evaluating the spin Hall conductivity. Focusing on the high frequency regime,
we obtain a diagonalized Hamiltonian. After getting the corresponding spectrum,
we show that there is a Hall conductivity without an external magnetic field,
which is noncommutativity parameter \theta-dependent. This allows us to make
contact with the spin Hall effect and also give different interpretations.
Fixing \theta, one can recover three different approaches dealing with the
phenomenon.
