A perturbation approach to finite difference methods
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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.
KeywordsFinite differences Quantum mechanics Energy levels
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