Propagation of Electronic Excitation in Insulating Crystals

A general method for the description of nonstationary excited states of an insulating crystal is outlined. For the general case, the time-dependent wave function is given implicitly by means of a simple generating function. In the nearest-neighbor approximation, the solution can be given explicitly in terms of Bessel functions. The effect of an idealized crystal surface on exciton propagation is examined. The exciton behaves as though repelled by the surface.