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A new finite difference scheme adapted to the one-dimensional Schrödinger equation (1993)

Geurts, Bernard J.

Springer

Zeitschrift für angewandte Mathematik und Physik 44 (1993), S. 654-672

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ISSN: 1420-9039

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00948481

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