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

作者：Frederick Ira Moxley III; Fei Zhu; Weizhong Dai

来源：American Journal of Computational Mathematics (AJCM), 2012, 02(03): 163-172.

DOI：10.4236/ajcm.2012.23022

• Schrodinger Equation
• Absorbing Boundary
• FDTD Method
• Stability

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.

• 出版日期2012