title: Numerical solutions of the Schrödinger equation with source terms or time-dependent potentials.
abstract: We develop an approach to solving numerically the time-dependent Schrödinger equation when it includes source terms and time-dependent potentials. The approach is based on the generalized Crank-Nicolson method supplemented with an Euler-MacLaurin expansion for the time-integrated nonhomogeneous term. By comparing the numerical results with exact solutions of analytically solvable models, we find that the method leads to precision comparable to that of the generalized Crank-Nicolson method applied to homogeneous equations. Furthermore, the systematic increase in precision generally permits making estimates of the error.
authors.affiliation: Department of Physics, Redeemer University College, Ancaster, Ontario L9K 1J4, Canada and Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada.
authors.forename: W
authors.initials: W
authors.lastname: van Dijk
authors.affiliation: Department of Computer Science, Kyoto Sangyo University, Kyoto 603-8555, Japan.
authors.forename: F M
authors.initials: FM
authors.lastname: Toyama