B. Jazbi and M. Moini, “On the Numerical Solution of One Dimensional Schr?dinger Equation with Boundary Conditions Involving Fractional Differential Operators,” IUST International Journal of Engineering Science, Vol. 19, 2008, pp. 21-26.

has been cited by the following article:

• 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.