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WKB-BASED SCHEMES FOR TWO-BAND SCHR¨ODINGER EQUATIONS IN THE HIGHLY OSCILLATORY REGIME

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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 Schr¨odinger 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. 

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