Time-dependent Schrödinger equation method: Application to charge transfer and excitation in H andH+collisions

Abstract

We have studied the excitation and charge transfer (including resonant charge transfer) processes of H and ${\mathrm{H}}^{+}$ collisions in a wide range of collision energies by solving the time-dependent Schr\"odinger equation with the classical trajectory approximation for the projectile. The time-dependent Schr\"odinger equation is solved by the split-operator method with a generalized pseudospectral (nonuniform grid) method. The calculated impact excitation and charge transfer cross sections are in reasonable agreement with the available experimental measurements. Such a time-dependent Schr\"odinger equation method can be used to study atom-ion collisions in a wide range of collision energies. Moreover, the time-dependent Schr\"odinger equation method can provide more dynamic information and physical insights. Combined with time-dependent density functional theory, our time propagator holds significant promise for many-electron processes in the interactions of highly charged ions with atoms, molecules, and solids.