The mixed quantum/classical molecular dynamics approach is employed to simulate the process in which an energetic H atom penetrates a Pd(100) surface. The H atom is described by a quantum wave packet, while all the Pd atoms are treated classically. Results from both 2D and 3D wave packet simulations are presented. It is found that the relaxation of the Pd lattice has minimal effect on the observed behavior, due to the lack of efficient energy flow between the light H atom and the heavy Pd atoms. Surprisingly, distinctly different behavior occurred in two and three dimensions, with the increased dimensionality exhibiting less surface penetration. The drastic difference may be traced back to the quantum mechanical nature of the motion of the H atom. Finally, the transport behavior of H in solids is discussed in connection with the simulation results.