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

    Research output: Contribution to journalArticleAcademicpeer-review

    49 Downloads (Pure)

    Abstract

    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
    Volume44
    Issue number4
    DOIs
    Publication statusPublished - 1993

    Keywords

    • METIS-140901
    • IR-85952

    Fingerprint Dive into the research topics of 'A new finite difference scheme adapted to the one-dimensional Schrodinger equation'. Together they form a unique fingerprint.

    Cite this