Lattice, Time-Dependent Schrödinger Equation Solution for Ion-Atom Collisions

Utilizing a lattice representation of the wave function and operators, we have solved the time-dependent Schr\"odinger equation over a wide range of collision energies and impact parameters to study excitation to low-lying states in collisions of protons with atomic hydrogen. The technique circumvents many of the shortcomings of commonly applied close coupling and perturbation theory approaches that are valid only in restricted regimes. Thus, the investigation represents a step towards precise knowledge of the dynamical quantities characterizing this and other fundamental collisions.