TITLE:
A Generalized FDTD Method with Absorbing Boundary Condition for Solving a Time-Dependent Linear Schrodinger Equation
AUTHORS:
Frederick Ira Moxley III, Fei Zhu, Weizhong Dai
KEYWORDS:
Schrodinger Equation; Absorbing Boundary; FDTD Method; Stability
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.2 No.3,
September
28,
2012
ABSTRACT: 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.