A new method is described for the solution of the single-particle Schrödinger equation in which the potential is nonspherical. This method is more efficient than methods based on spherical-harmonic expansions, both in terms of computer time and storage. The method is distinguished by the use of a "ray" representation in which (a) the potential is diagonal, (b) the nondiagonal portion of the Laplacian is small, and (c) boundary conditions are easily imposed. Illustrative applications to the orbital and total energies of free atoms are described. © 1981 The American Physical Society.