A consistent approach to atom--surface-energy transfer in one dimension is presented. A semigroup technique is employed to establish equations of motion for a quantal phonon reservoir, which is coupled to the propagation of a wave packet. The time-dependent Schroedinger equation is solved using a pseudospectral technique. The average energy transfer to the bath is then determined. This study supersedes conventional perturbative treatments and reveals the utility of one-dimensional models in the study of particle-surface collisions at low energies.