A Generalized FDTD Method with Absorbing Boundary Condition for Solving a Time-Dependent Linear Schrodinger Equation

• 作者: Fei Zhu Frederick Ira Moxley III Weizhong Dai
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: SCHRODINGER Equation Absorbing Boundary FDTD Method Stability
• 年，卷（期）: 2012,（3）
• 页码范围: 163-172
• 页数: 10页
• 分类号: O1

摘要

The Finite-Difference Time-Domain (FDTD) method is a well-known technique for the analysis of quantum devices. It solves a discretized Schrodinger equation in an iterative process. However, the method provides only a second-order accurate numerical solution and requires that the spatial grid size and time step should satisfy a very restricted condition in order to prevent the numerical solution from diverging. In this article, we present a generalized FDTD method with absorbing boundary condition for solving the one-dimensional (1D) time-dependent Schr?dinger equation and obtain a more relaxed condition for stability. The generalized FDTD scheme is tested by simulating a particle moving in free space and then hitting an energy potential. Numerical results coincide with those obtained based on the theoretical analysis.