Contributions to Books:
J. Geier, A. Arnold:
"WKB-based schemes for two-band Schrödinger equations in the highly oscillatory regime";
in: "ASC Report 25/2011",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
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 WKB-type transformation, which filters out the
dominant oscillations. The resulting ODE-system is much smoother and can hence be discretized on a much
coarser grid, with significantly reduced numerical costs.
Here we are concerned with stationary two-band Schršodinger equations employed in quantum transport
applications. We focus on the Kane-model and the two band k·p-model. The accuracy of the presented
method is illustrated on a numerical example.
Schršodinger equation, Kane-model, two-band k · p-model, highly oscillating wave functions,
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.