Abstract: A Broyden method,which has been used in the device simulation domain,is described and used to self-consistently solve the electron density and electric potential of a 1D semiconductor quantum line.Results are compared to those obtained by the SOR method (Newton method).The convergence rates of these two methods are also compared.The Broyden method yields an accurate results using fewer iteration steps.Thus the Broyden method can greatly accelerate the process of solving Schrodinger and Poisson nonlinear equation systems.

Key words: Broyden method, Schrodinger equation, Poisson equation, self-consistent solution