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An iterative method to calculate the phases of Coulomb functions

Published online by Cambridge University Press:  24 October 2008

P. De A. P. Martins
P. De A. P. Martins
Affiliation:
University College, London†
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Abstract

The differential equation

defining the function of the amplitude sL is integrated by an iterative procedure. An expression for the phase

is obtained in terms of integrals of ωL and its derivatives. The method is applied to the numerical calculation of Coulomb functions and the accuracy of the results is discussed. Recurrence relations are used to obtain øL, L ≽ 1.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 69 , Issue 1 , January 1971 , pp. 167 - 173
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

REFERENCES

(1)Burgess, A.Proc. Phya. Soc. 81 (1963), 442–452.CrossRefGoogle Scholar
(2)Martins, P. de A. P.J. Phys. B (Proc. Phya. Soc.) 1 (1968), 154–162.Google Scholar
(3)Seaton, M. J. and Peach, G.Proc. Phya. Soc. 79 (1962), 1296–1297.CrossRefGoogle Scholar