  The Quantum Mechanics of a point particle on a Noncommutative Plane in a
magnetic field is implemented in the present work as a deformation of the
algebra which defines the Landau levels. I show how to define, in this deformed
Quantum Mechanics, the physical observables, like the density correlation
functions and Green function, on the completely filled ground level. Also it
will be shown that the deformation changes the effective magnetic field which
acts on the particles at long range, leading to an incompressible fluid with
fractional filling of Laughlin type.
