van Dijk W, Toyama F M
Department of Physics, Redeemer University College, Ancaster, Ontario L9K 1J4, Canada and Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada.
Department of Computer Science, Kyoto Sangyo University, Kyoto 603-8555, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Dec;90(6):063309. doi: 10.1103/PhysRevE.90.063309. Epub 2014 Dec 17.
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.
