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S. Descomb and M. Thalhammer, “An Exact Local Error Representation of Exponential Operator Splitting Methods for Evolutionary Problems and Applications to Linear Schr?dinger Equations in the Semi-Classical Regime,” BIT Numer Math, Vol. 50, 2010, pp. 729-749.

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.