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 Schrodinger 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.