Author(s)

Frederick Ira Moxley III, Fei Zhu, Weizhong Dai

Department of Mathematics & Statistics, Louisiana Tech University, Ruston, USA.
Department of Physics, Louisiana Tech University, Ruston, USA.

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.

Schrodinger Equation; Absorbing Boundary; FDTD Method; Stability

Moxley III, F. , Zhu, F. and Dai, W. (2012) A Generalized FDTD Method with Absorbing Boundary Condition for Solving a Time-Dependent Linear Schrodinger Equation. American Journal of Computational Mathematics, 2, 163-172. doi: 10.4236/ajcm.2012.23022.