The symmetry of the two- and three-dimensional Schrodinger equation is analysed in terms of second-order differential operators which commute with the Hamiltonian of the solutions of the stationary Schrodinger equation. A set of equations for the coefficients of the symmetry operators is formulated and a general form for the structure of the symmetry operators is obtained. Symmetry operators have been found for the cases of some potentials. The effect of the symmetry raising at zero energy is described.