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Numerical solutions of the Schrödinger equation with source terms or time-dependent potentials
1Department of Physics, Redeemer University College, Ancaster, Ontario L9K 1J4, Canada and Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada.
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.
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