On the Twofold Moutard Transformation of the Stationary Schrödinger Equation with Axial Symmetry

The generalized Moutard transformation of the stationary axially symmetric Schrödinger equation is considered. It is shown that a superposition of two Moutard transformations can provide new potentials for the eigenvalue problem. Examples of two-dimensional potentials and exact solutions for the stationary axially symmetric Schrödinger equation are obtained as an application of the twofold Moutard transformation.