TY - JOUR
T1 - Absorbing Boundary Conditions for Variable Potential Schrödinger Equations via Titchmarsh-Weyl Theory
AU - Ehrhardt , Matthias
AU - Zheng , Chunxiong
JO - Communications in Computational Physics
VL - 3
SP - 711
EP - 728
PY - 2025
DA - 2025/08
SN - 38
DO - http://doi.org/10.4208/cicp.OA-2024-0178
UR - https://global-sci.org/intro/article_detail/cicp/24313.html
KW - Absorbing boundary conditions, variable potential, Schrödinger equation, Titchmarsh-Weyl $m$-function, unbounded domain.
AB - <p style="text-align: justify;">We propose a novel approach to simulate the solution of the time-dependent
Schrödinger 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.</p>