ENVELOPE-FUNCTION THEOREM IN THE HIGH-ENERGY LIMIT

The envelope-function theorem is considered in the limit that electron energy far exceeds that of the characteristic height of the potential array which, in turn, is comprised of a slowly varying component and smaller amplitude rapidly varying component. Working in the nearly-fre e-electron model, it is found that ''new'' energies and wave functions at band edges are those related to the slowly varying component of th e potential. Wave functions related to the rapidly varying potential c omponent average to zero over a small function of a primitive cell. Th ese properties comprise the envelope-function theorem relevant to high -energy charge carriers passing through a quantum well array. (C) 1995 American Institute of Physics.