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Journal of Mathematical Chemistry

, Volume 48, Issue 4, pp 1036–1043 | Cite as

A perturbation approach to finite difference methods

  • J. P. Killingbeck
  • A. Lakhlifi
Original Paper

Abstract

A perturbation theoretic approach to finite difference methods for the calculation of eigenvalues is shown to permit an increase in the accuracy of the calculations and also to make possible the calculation of expectation values along with the eigenvalues. An application of the virial theorem can then boost the order of accuracy of any given finite difference method. Integrated probabilities and point values of the normalized wavefunction can be found without any use of quadratures. Illustrative examples are given involving the Schrodinger equation for simple polynomial potentials.

Keywords

Finite differences Quantum mechanics Energy levels 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Centre for MathematicsUniversity of HullHullUK
  2. 2.Institut UTINAM (CNRS UMR 6213)Besancon cedexFrance

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