A Full Newton Scheme for the Coupled Schr ö dinger, Poisson, and Density-gradient Equations

We develop a fully coupled Newton scheme for the self-consistent solution of the Schrödinger, Poisson, and transport equations, which is found to be a powerful method in several moderate sized problems. We apply the method to a new hybrid model that solves the one-dimensional Schrödinger equation in the confinement direction and the quantum corrected transport equation in the transport direction, and study the convergence behavior of the coupled scheme. Also, we check the validity of our new model using the nonequilibrium Green´s function method.