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We develop an approach to solving numerically the time-dependent Schrodingerequation when it includes source terms and time-dependent potentials. Theapproach is based on the generalized Crank-Nicolson method supplemented with anEuler-MacLaurin expansion for the time-integrated nonhomogeneous term. Bycomparing the numerical results with exact solutions of analytically solvablemodels, we find that the method leads to precision comparable to that of thegeneralized Crank-Nicolson method applied to homogeneous equations.Furthermore, the systematic increase in precision generally permits makingestimates of the error.

Numerical solutions of the Schrodinger equation with source terms or time-dependent potentials