  We propose an approach based on the generalized quantum mechanics to deal
with the basic features of the spin Hall effect. We begin by considering two
decoupled harmonic oscillators on the noncommutative plane and determine the
solutions of the energy spectrum. We realize two algebras in terms of the
quadratic observables and show their importance in filling the shells with
fermions. Under some transformation we show that our system is submitted to an
effective Lorentz force similar to that acting on one particle in an external
magnetic field. From equation of motions, we end up with the charge and spin
Hall conductivities as function of the noncommutative parameter \theta. By
switching off \theta we recover standard results developed on the subject and
in the limit \theta --> 0 we show that our approach can reproduce the Laughin
wavefunctions.
