State-to-state transition probabilities for time-dependent Hamiltonians using complex absorbing potentials

. Earlier work has derived a new expression for the time-independent scattering probability for time-dependent Hamiltonians for cases where the motion is free at infinitely large times. Here we introduce a new technique which provides an efficient numerical algorithm for the calculation of multiphoton event probabilities based on using complex absorbing potentials along the scattering coordinate. The (t, t # ) method is used allowing an analytical propagation of the initial state and avoiding long propagation times and accumulation of numerical errors. An iterative technique for the solution of non-Hermitian linear systems is used which allows us to tackle large time-dependent systems, both in internal degrees of freedom and in the number of Fourier components in the time-dependent potential term. A numerical example illustrating the usefulness of the theory is given. 1. Introduction Numerical solution of the time-dependent Schr odinger equation has become one of the main tools of mol...