Institute of Mathematics,

University of Bialystok,

2 Akademicka Str.,

15-267 Bialystok,

POLAND

E-mail: tomczyz@math.uwb.edu.pl

**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.