2015/06/26 by Matthias Geilhufe, R. Matthias Geilhufe, Steven Achilles +8
Mathematics · Physics and Astronomy · #Algorithm #Atomic and Molecular Physics #Coulomb #Coulomb wave function #Electric potential #Electron #Mathematical analysis #Mathematics #Mathieu function #Numerical analysis #Physics #Potential method #Quantum Chromodynamics and Particle Interactions #Quantum Mechanics and Non-Hermitian Physics #Quantum electrodynamics #Quantum mechanics #Scattering #cond-mat.mtrl-sci #physics.comp-ph
paper · pdf · doi:10.1088/0953-8984/27/43/435202
published as J. Phys.: Condens. Matter 27 435202, 2017 · 16 pages, 6 figures, preprint
arxiv created 2015/06/26 · openalex publication_date 2015/10/08 · arxiv updated 2017/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
For a reliable fully-relativistic Korringa-Kohn-Rostoker Green function method, an accurate solution of the underlying single-site scattering problem is necessary. We present an extensive discussion on numerical solutions of the related differential equations by means of standard methods for a direct solution and by means of integral equations. Our implementation is tested and exemplarily demonstrated for a spherically symmetric treatment of a Coulomb potential and for a Mathieu potential to cover the full-potential implementation. For the Coulomb potential we include an analytic discussion of the asymptotic behaviour of irregular scattering solutions close to the origin (r << 1).