ITERATION SCHEME FOR THE SOLUTION OF THE TWO-DIMENSIONAL SCHRODINGER-POISSON EQUATIONS IN QUANTUM STRUCTURES

摘要: A fast and robust iterative method for obtaining self-consistent solutions to the coupled system of Schrodinger’s Poisson’s equations is presented. Using quantum mechanical perturbation theory, a simple expression describing dependence electron density on electrostatic potential derived. This then used implement an iteration scheme, based predictor-corrector type approach, solution differential equations. We find that this approach simplifies software implementation nonlinear problem, provides excellent convergence speed stability. demonstrate by presenting example calculation two-dimensional bound states within cross section GaAs-AlGaAs wire. For example, six times faster applying our compared corresponding underrelaxation algorithm.