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ORIGINAL RESEARCH article

Front. Phys.
Sec. Condensed Matter Physics
Volume 12 - 2024 | doi: 10.3389/fphy.2024.1393130

On the calculation of irregular solutions of the Schr ödinger equation for non-spherical potentials

Provisionally accepted
Rudolf Zeller Rudolf Zeller *
  • Julich Research Center, Helmholtz Association of German Research Centres (HZ), Jülich, Germany

The final, formatted version of the article will be published soon.

    The irregular solutions of the stationary Schr ödinger 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.

    Keywords: Schr ödinger equation, non-spherical potentials, scattering theory, Irregular solutions, Boundary conditions, Integral-equation method, Chebyshev solver

    Received: 28 Feb 2024; Accepted: 16 May 2024.

    Copyright: © 2024 Zeller. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Rudolf Zeller, Julich Research Center, Helmholtz Association of German Research Centres (HZ), Jülich, Germany

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