Several effects due to the coupling of the translational motion of a gas phase atom (H), to the vibrations of a substrate [Cu(100)], are investigated here with time-dependent wave packet methods. Three different propagation techniques, namely, reduced-dimensionality but "exact" wave packet propagation, the time-dependent-self-consistent-field (TDSCF) method, and the "mean-field" (Ehrenfest) mixed quantum-classical-molecular-dynamics scheme (QCMD), are tested against each other and compared with classical trajectory results, and with rigid-surface calculations. Our key findings are: (1) The Cu(100) substrate is very "open" for impinging H atoms, leading to large subsurface and bulk absorption yields; (2) the H atoms can be "hot" for several picoseconds after hitting the surface before they finally settle down in adsorption or absorption sites; (3) while classical mechanics agrees reasonably well with the exact quantum calculation, the mixed quantum-classical and TDSCF approaches which both rely on a single-configuration ansatz for the total nuclear wave function, grossly underestimate the coupling between the H atom and the surrounding Cu atoms; (4) all (approximate) methods agree in the fact that by taking more substrate vibrations into account, the reflection probability diminishes while sticking increases.