有限差分–配点法求解SchrO¨dinger方程
Finite Difference-Collocation Method for the SchrO¨dinger Equation
摘要: 本文将重心插值配点法结合Crank-Nicolson差分格式求解线性Schrödinger方程。首先，对方程中的空间方向上采用重心插值Chebyshev配点格式进行离散，时间方向采用Crank-Nicolson差分格式，从而导出对应的代数方程组。最后，数值算例验证该计算格式具有高精度性，并且满足质量和能量守恒性。
Abstract: In this paper, the barycentric interpolation collocation method combined with Crank-Nicolson dif-ference scheme is used to solve the linear Schrödinger equation. Firstly, the space direction is dis-cretized by the Chebyshev collocation method of barycentric interpolation, and the time direction is discretized by the Crank-Nicolson difference scheme. Finally, numerical examples show that the numerical scheme has high precision and satisfies the conservation of mass and energy.
文章引用：孙浩然, 黄思雨, 周铭扬, 李依伦. 有限差分–配点法求解SchrO¨dinger方程[J]. 应用数学进展, 2022, 11(5): 3150-3163. https://doi.org/10.12677/AAM.2022.115334

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