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

has been cited by the following article:

• TITLE: Simulation of Time-Dependent Schrödinger Equation in the Position and Momentum Domains

  AUTHORS: Michael Jennings

  KEYWORDS: Schrödinger Equation, Predictor-Corrector, Fourier Transform, Momentum Domain

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.5 No.3, September 7, 2015

  ABSTRACT: The paper outlines the development of a new, spectral method of simulating the Schrödinger equation in the momentum domain. The kinetic energy operator is approximated in the momentum domain by exploiting the derivative property of the Fourier transform. These results are compared to a position-domain simulation generated by a fourth-order, centered-space, finite-difference formula. The time derivative is approximated by a four-step predictor-corrector in both domains. Free-particle and square-well simulations of the time-dependent Schrödinger equation are run in both domains to demonstrate agreement between the new, spectral methods and established, finite-difference methods. The spectral methods are shown to be accurate and precise.