Time dependent quantum mechanical theory of gas–surface energy transfer

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Abstract
A fully quantum mechanical theory for phonon inelastic gas–surface scattering is presented. Both surface and bulk phonons are coupled to the molecule via perturbation theory. The reduced density matrix of the molecule is written in terms of three wave-function-like objects, which obey Schrodinger-like equations of motion. These highly coupled equations of motion are evolved simultaneously in time, using standard techniques. The method can be applied to any of several recent quantum and semiclassical time dependent scattering theories, and allows one to compute the thermally averaged properties of the system at all times. The total computational effort is only about three times that of the zero temperature calculation. Results are presented for the inelastic scattering of He and Ne beams from Cu(111), Cu(100), and Ni(111).