Self-consistent trajectories for surface scattering via classical-quantal coupling

We present a set of coupled Schrödinger-Hamiltonian equations that may be solved to give self-consistent classical trajectories and quantal wave functions while conserving total energy and momentum during time-dependent simulations of electronic systems. As a first nontrivial application, we examine the collision of an atom with an infinite barrier. Our results clearly demonstrate the necessity for and importance of classical-quantal coupling in low-energy scattering.