On the calculation of irregular solutions of the Schr\"odinger equation for non-spherical potentials

Abstract

The irregular solutions of the stationary Schr\"odinger equation are important for the fundamental formal development of scattering theory. They are also necessary for the analytical properties of the Green function, which in practice can speed up calculations enormously. Despite these facts they are seldom considered in numerical treatments. The reason for this is their divergent behavior at the origin. This divergence demands high numerical precision that is difficult to achieve, in particular, for non-spherical potentials which lead to different divergence rates in the coupled angular momentum channels. Based on an unconventional treatment of boundary conditions, an integral-equation method is developed, which is capable to deal with this problem. The available precision is illustrated by electron-density calculations for NiTi in its monoclinic B19' structure.