A NEW FINITE-DIFFERENCE SCHEME ADAPTED TO THE ONE-DIMENSIONAL SCHRODINGER-EQUATION

We present a new discretisation scheme for the Schrodinger equation ba sed on analytic solutions to local linearisations. The scheme generate s the normalised eigenfunctions and eigenvalues simultaneously and is exact for piecewise constant potentials and effective masses. Highly a ccurate results can be obtained with a small number of mesh points and a robust and flexible algorithm using continuation techniques is deri ved. An application to the Hartree approximation for SiGe heterojuncti ons is discussed in which we solve the coupled Schrodinger-Poisson mod el problem selfconsistently.