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Eigenvalue problems treated by finite-difference methods. II. Two-dimensional Schrödinger equations

Published online by Cambridge University Press:  24 October 2008

H. C. Bolton  and
H. I. Scoins
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Abstract

A discussion is given of the convergence of the eigenvalues Λ (N) of two-dimensional finite-difference equations towards the eigenvalues Λ of the corresponding second-order differential equation, and it is shown that

where h = N−1 and ν2 is a constant. As in our previous paper (4), this can be used to make an accurate estimate of λ by extrapolating to h = 0. After an account of the relaxation method used for computing Λ(N) and a discussion of the residual vector, results are presented for an approximation to the lowest spatially symmetric and antisymmetric states of two electrons in a sphere, interacting through their Coulomb potential.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 53 , Issue 1 , January 1957 , pp. 150 - 161
Copyright
Copyright © Cambridge Philosophical Society 1957

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References

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