AI 中文总结
该研究针对模拟一维量子晶格的薛定谔方程构造精确透明边界条件，推导卷积型边界条件并验证其一致性，提出时间离散方案，实验证明其可消除虚假背散射、保持高斯波包无反射传播。
AI 中文摘要
我们为模拟一维量子晶格的时间连续、空间离散薛定谔方程构造精确透明边界条件（TBCs）。利用离散系统新近得到的精确解，通过拉普拉斯变换解析推导Dirichlet-to-Neumann映射，得到由贝塞尔函数控制的卷积型边界条件。我们严格证明该离散形式在连续极限下与连续对应形式的一致性，还提出基于梯形法则的高效时间离散方案用于实际实现。采用Crank-Nicolson求解器的数值实验验证，所提TBCs完全消除虚假背散射，保持高斯波包离开计算域时的无反射传播。
英文摘要
We construct exact transparent boundary conditions (TBCs) for a time-continuous, spatially discrete Schrödinger equation that models a one-dimensional quantum lattice. Using a recently developed exact solution for the discrete system, we derive the Dirichlet-to-Neumann maps analytically via Laplace transforms. This yields a convolution-type boundary condition governed by Bessel functions. We rigorously demonstrate the consistency of this discrete formulation with its continuous counterpart in the continuum limit. Additionally, we present an efficient time-discretization scheme based on the trapezoidal rule for practical implementation. Numerical experiments using a Crank-Nicolson solver verify that our proposed TBCs eliminate spurious backscattering entirely and preserve reflectionless propagation of a Gaussian wave packet exiting the computational domain
Comments10 pages, 3 figures
