Calculation of scattering wave functions by a numerical procedure based on the Møller wave operator

We present a procedure that numerically evaluates the scattering wave function. The solution to the time-independent Schrödinger equation is calculated by a novel combination of: (a) the Møller operator of scattering theory, (b) time-dependent wave packets whose shape is unconstrained, and (c) efficient wave packet propagation on a dynamically-adapted grid. The superposition of packets appropriate to the scattering boundary conditions yields the full wave function, from which scattering amplitudes are then obtained. Since the procedure does not make use of basis-set expansions, its computational cost is independent of the number of open channels. It explicitly calculates the wave function not only in the asymptotic region but also within the interaction region, so it allows one to evaluate additional information beyond the scattering amplitude, as well as the functional sensitivity of transition probabilities with respect to changes in the potential. Applications here are illustrated by two simple examples: one-dimensional tunneling through a potential barrier, and elastic scattering from a one-dimensional periodic surface (i.e., a two-dimensional scattering problem). Extensive applications to imperfect surfaces including sensitivity analysis are separately presented in another article.