  The motion of a charged particle moving on a flat surface is studied through
the constants of motion associated to the system, given the magnetic gauge. The
usual Landau' solution and the non separable solution for the Landau's gauge
are found, and new non separable solution for the symmetric gauge is given. As
a consequence of this, the quantization of the magnetic flux results from the
invariance of the solutions under the unitary transformations which arise from
the operators constants of motion.
