Invariance of the Schr\"odinger equation with respect to group transformations with discrete parameter

Abstract:
We find the algebra of symmetry for Schr\"odinger equation with potential dependent on time and we show, how to apply it to generate new solutions and potentials for this equation. We also propose the method for construction of potentials in the Schr\"odinger equation for which this equation is invariant with respect to the group transformations with discrete parameters.