Symmetries and supersymmetries of generalized Schrodinger equations

Abstract

The contemporary results concerning Lie symmetries, higher symmetries and supersymmetries in generalized Schr\"odinger equations are presented. Namely, the standard Schr\"odinger equation with scalar and vector potentials and position dependent mass Schr\"odinger equations are discussed as well as the equations with matrix potentials. Group classification of the mentioned equations is carried out, i.e., all inequivalent versions of them are presented together with the admitted Lie symmetries. An extended class of exactly solvable quantum mechanical problems admitting higher symmetries and supersymmetries is specified.