Optical potentials in time-dependent quantum theory

The equations governing the exact quantum mechanical time evolution of a projected portion of the wave function are derived in terms of an optical potential. Although these equations are non-Markoffian, they are solved numerically for two types of approximate optical potential for the model problem of the linearly forced harmonic oscillator. It is shown that the perturbation optical potential is superior to normal second order perturbation theory and may be useful in semiclassical scattering problems, etc.