  Using elements of symmetry, we constructed the Noncommutative Schr\"odinger
Equation from a representation of Exotic Galilei Group. As consequence, we
derive the Ehrenfest theorem using noncommutative coordinates. We also have
showed others features of quantum mechanics in such a manifold. As an important
result, we find out that a linear potential in the noncommutative Schr\"odinger
equation is completely analogous to the ordinary case. We also worked with
harmonic and anharmonic oscillators, giving corrections in the energy for each
one.
