A new finite difference scheme adapted to the one-dimensional Schrodinger equation

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    We present a new discretisation scheme for the Schrödinger equation based on analytic solutions to local linearisations. The scheme generates the normalised eigenfunctions and eigenvalues simultaneously and is exact for piecewise constant potentials and effective masses. Highly accurate results can be obtained with a small number of mesh points and a robust and flexible algorithm using continuation techniques is derived. An application to the Hartree approximation for SiGe heterojunctions is discussed in which we solve the coupled Schrödinger-Poisson model problem selfconsistently.
    Original languageEnglish
    Pages (from-to)654-672
    Number of pages19
    JournalZeitschrift für angewandte Mathematik und Physik
    Issue number4
    Publication statusPublished - 1993



    • METIS-140901
    • IR-85952

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