AUTHOR=Zeller Rudolf TITLE=On the calculation of irregular solutions of the Schrödinger equation for non-spherical potentials with applications to metallic alloys JOURNAL=Frontiers in Physics VOLUME=12 YEAR=2024 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2024.1393130 DOI=10.3389/fphy.2024.1393130 ISSN=2296-424X ABSTRACT=

The irregular solutions of the stationary Schrödinger 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 greatly speed up calculations. Nevertheless, they are seldom considered in numerical treatments because of their divergent behavior at origin. This divergence demands high numerical precision that is difficult to achieve, particularly 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 here developed which is capable of dealing with this problem. The available precision is illustrated by electron-density calculations for NiTi in its monoclinic B19’ structure.