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arXiv · 2408.00671

Absorbing Boundary Conditions for Variable Potential Schr\"odinger Equations via Titchmarsh-Weyl Theory

Matthias Ehrhardt·Chunxiong Zheng
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Abstract

We propose a novel approach to simulate the solution of the time-dependent Schr\"odinger equation with a general variable potential. The key idea is to approximate the Titchmarsh-Weyl m-function (exact Dirichlet-to-Neumann operator) by a rational function with respect to an appropriate spectral parameter. By using this method, we overcome the usual high-frequency restriction associated with absorbing boundary conditions in general variable potential problems. The resulting fast computational algorithm for absorbing boundary conditions ensures accuracy over the entire frequency range.

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Matthias Ehrhardt, Chunxiong Zheng. 2024-08-01. Absorbing Boundary Conditions for Variable Potential Schr\"odinger Equations via Titchmarsh-Weyl Theory. https://arxiv.org/abs/2408.00671

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