Dresden 2003 – wissenschaftliches Programm

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SYCN: Computational nanoscience - from materials to biology

SYCN 102: Computational Nanoscience: From Materials to Biology (Poster, gemeinsam mit SYSE)

SYCN 102.7: Poster

Dienstag, 25. März 2003, 19:00–21:00, ZEU/160

New adapted method for solving systems of differential equations - The Magnus method — •Markus Däne¹, Jörg Wensch², Arthur Ernst³, Wolfram Hergert¹, and Rüdiger Weiner² — ¹Universität Halle-Wittenberg, Fachbereich Physik — ²Universität Halle-Wittenberg, Fachbereich Mathematik und Informatik — ³Max Planck Institute of Microstructure Physics, Halle

A basic problem in quantum chemistry or density functional theory (DFT) is the solution of the Schrödinger equation or Dirac equation for given potentials numerically. A series of methods is already proposed, tuned for special cases of application.

We present a new method which is adapted to a special class of differential equations with exponentially decaying or oscillatory solutions. The Magnus-method allows under optimal conditions step sizes larger than one oscillation period. Systems of differential equations of different orders can be solved with the same algorithm. Although the mathematical backgroud of the method is complex the implementation is straightforward.

We will demonstrate that the Magnus-Method can be applied to solve the Schrödinger equation or the Dirac equation in solid state theory for bound states and scattering problems.