Absorbing Boundary Conditions for Variable Potential Schr\"odinger Equations via Titchmarsh-Weyl Theory
<|reference_start|>Absorbing Boundary Conditions for Variable Potential Schr\"odinger Equations via Titchmarsh-Weyl Theory: 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.<|reference_end|>
@article{ehrhardt2024absorbing,
    title={Absorbing Boundary Conditions for Variable Potential Schr\"odinger
  Equations via Titchmarsh-Weyl Theory},
    author={Matthias Ehrhardt and Chunxiong Zheng},
    journal={arXiv preprint arXiv:2408.00671},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.00671},
    primaryClass={math.NA cs.NA physics.comp-ph}
}