Uniform semiclassical self-consistent field and adiabatic calculations of complex energy eigenvalues for nonseparable systems

Abstract

The semiclassical self-consistent field (SCF) procedure is extended to the calculation of complex energy eigenvalues corresponding to metastable resonant states. By use of the complex Hellmann–Feynman theorem a fully uniform SCF procedure is developed which is equally suitable for states lying below or above any barriers in the potential, and, unlike the primitive semiclassical SCF originally developed by Ratner, Gerber, and co-workers, undergoes a smooth transition through the barrier top region. A detailed numerical investigation is presented for a coupled double barrier problem supporting no bound states. Comparison is made with uniform semiclassical calculations based on an adiabatic separation of the wave function as well as with accurate quantum complex coordinate SCF calculations, and quantum CI results available in the literature. Our calculations allow a comparison of the usefulness of the SCF and adiabatic approximations in predicting mode specificity.