Lattice, time-dependent Schrodinger equation solution for ion-atom collisions

Utilizing a lattice representation of the wave function and operators, we h ave solved the time-dependent Schrodinger equation over a wide range of col lision energies and impact parameters to study excitation to low-lying stat es in collisions of protons with atomic hydrogen. The technique circumvents many of the shortcomings of commonly applied close coupling and perturbati on theory approaches that are valid only in restricted regimes. Thus, the i nvestigation represents a stop towards precise knowledge of the dynamical q uantities characterizing this and other fundamental collisions.