 
Summary: NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2011, 1 (1), P. 122
UDC nan
WKBbased schemes for twoband Schr¨odinger
equations in the highly oscillatory regime
Jens Geier1
, Anton Arnold1
1
Institute for Analysis and Scientific Computing, Vienna University of Technology,
Wiedner Hauptstr. 8, A1040 Wien, Austria.
jens.geier@tuwien.ac.at, anton.arnold@tuwien.ac.at
PACS 02.60.Lj, 02.60.Lh, 85.30.De
An efficient and accurate numerical method is presented for the solution of highly oscillatory differential
equations in one spatial dimension. While standard methods would require a very fine grid to resolve the
oscillations, the presented approach uses first an analytic WKBtype transformation, which filters out the
dominant oscillations. The resulting ODEsystem is much smoother and can hence be discretized on a much
coarser grid, with significantly reduced numerical costs.
Here we are concerned with stationary twoband Schr¨odinger equations employed in quantum trans
port applications. We focus on the Kanemodel and the two band k·pmodel. The accuracy of the presented
method is illustrated on a numerical example.
Keywords: Schr¨odinger equation, Kanemodel, twoband k · pmodel, highly oscillating wave functions,
