  We study symmetry properties of the Schr\"odinger equation with the potential
as a new dependent variable, i.e., the transformations which do not change the
form of the class of equations. We also consider systems of the Schr\"odinger
equations with certain conditions on the potential. In addition we investigate
symmetry properties of the equation with convection term. The contact
transformations of the Schr\"odinger equation with potential are obtained.
