The transfer of charge when an atom or ion strikes a surface is considered within a simple model where both ion and electron can be treated fully quantum mechanically and on the same footing. Results for the dependence of the charge transfer on incident energy and potential parameters show that the predictions of a standard model where the ion is assumed to follow a classical trajectory and the charge transfer described in terms of a level width are in general quite reliable. Charge transfer also occurs via inelastic "shake-up" processes. We show that the behaviour of this fraction can be understood within a trajectory model where the action of the surface on the bound electron is treated via a time-dependent force.