Dresden 2011 – wissenschaftliches Programm
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A: Fachverband Atomphysik
A 21: Atomic systems in external fields II
A 21.4: Vortrag
Donnerstag, 17. März 2011, 14:45–15:00, BAR 205
(contribution withdrawn) Numerical solution of coupled radial ODE eigenvalue problems — •Robert Hammerling1 and Othmar Koch2 — 1Center Computational Material Science, TU Wien, A-1040, AUT — 2Institute for Analysis, TU Wien, A-1040, AUT
In the effective one-particle description of electronic structure within DFT one has to calculate eigenvalues of PDE Schrödinger operators. For deep lying core states normally only the local radial potential is used and therefore decoupled ODEs can be solved. In this contribution we present our non-perturbative approach (see e.g. Computer Physics Communications, 181, 1557) to the coupled radial equations in a non-spherical potential. We compare a few different solution methods, one-sided matrix shooting, two-sided matrix shooting, polynomial collocation strategies and basis set expansion methods. The studied test cases comprise the Hydrogen molecular ion treated in one-center approximation and the dc-Stark effect of the Hydrogen atom.
The work is part of a joint collaboration between mathematicians and physicists within the project 'Mathematik und .. 2007' sponsored by WWTF.