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On the corrector formulas for the numerical solution of the Schrödinger equation for central fields

Published online by Cambridge University Press:  24 October 2008

L. Lovitch  and
S. Rosati
L. Lovitch
Affiliation:
Istituto Nazionalc Fisica Nucleare, Sezione di Pisa, Italy
S. Rosati
Affiliation:
Istituto di Fisica, Università di Pisa, Istituto Nazionale Fisica Nucleare, Sezione di Pisa, Italy
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Extract

The evaluation of the eigenvalues and corresponding solutions of a Schrödinger equation is an ever-present problem in atomic and nuclear physics. For the numerical evaluation of the Schrödinger equation for a particle in a central potential, a useful corrector formula was derived by Douglas and Ridley ((5)) some years ago. Given a first estimate of the eigenvalue, this formula enables one to obtain a better estimate using any standard integration procedure for the differential equation. In a particular example, it was found ((5)) that it was necessary to start with an initial value which was accurate to about 10% in order that the procedure should converge to the desired eigenvalue, and that few iterations were required to obtain the eigenvalue with good precision.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 1 , January 1966 , pp. 79 - 82
Copyright
Copyright © Cambridge Philosophical Society 1966

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References

REFERENCES

(1)Cooley, J. W.Math. Comp. 15 (1961), 363.Google Scholar
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(3)Lovitch, L. and Rosati, S.Phys. Rev. (to be published).Google Scholar
(4)Löwdin, P. O.An elementary iteration-variation method for solving the Schrödinger equation. Technical Note from the Uppsala Chemistry Group, 1958, J. Molecular Spectroscopy 10 (1963), 12.CrossRefGoogle Scholar
(5)Ridley, E. C.Proc. Cambridge Philos. Soc. 51 (1955), 702.CrossRefGoogle Scholar