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arXiv · 1606.05207

Stationary Schrödinger equation in the semi-classical limit: numerical coupling of oscillatory and evanescent regions

Anton Arnold·Claudia Negulescu
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Abstract

This paper is concerned with a 1D Schrödinger scattering problem involving both oscillatory and evanescent regimes, separated by jump discontinuities in the potential function, to avoid "turning points". We derive a non-overlapping domain decomposition method to split the original problem into sub-problems on these regions, both for the continuous and afterwards for the discrete problem. Further, a hybrid WKB-based numerical method is designed for its efficient and accurate solution in the semi-classical limit: a WKB-marching method for the oscillatory regions and a FEM with WKB-basis functions in the evanescent regions. We provide a complete error analysis of this hybrid method and illustrate our convergence results by numerical tests.

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Anton Arnold, Claudia Negulescu. 2016-06-16. Stationary Schrödinger equation in the semi-classical limit: numerical coupling of oscillatory and evanescent regions. https://arxiv.org/abs/1606.05207

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