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Some Calculations relevant to the Quantum Defect in the Extended Ritz Formula

Published online by Cambridge University Press:  24 October 2008

J. Hargreaves
J. Hargreaves
Affiliation:
Clare College
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Extract

The object of this paper is to make certain calculations which will be required in the estimation of the quantum defect. Hartree has defined certain solutions Gi(σ, ζ), Hi(σ, ζ) of the wave equation for an electron in a Coulomb field, viz.

Type
Articles
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 25 , Issue 3 , July 1929 , pp. 315 - 322
Copyright
Copyright © Cambridge Philosophical Society 1929

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References

* Proc. Camb. Phil. Soc. xxiv, 426 (1928).Google Scholar

* See e.g Whittaker, and Watson, , Modern Analysis, pp. 354–357.Google Scholar

† See § 2 of the Precceding Paper by Dr D. R. Hartree

* Whittaker, and Watson, , he. cit., p. 376.Google Scholar

† See the appendix.

* Neumann, , Theorie der Besiel' schen Functionen (Leipzig, 1867), p. 52.Google Scholar The expansion and proof are given by Watson (Bessel Functions, 1922, p. 71). (There is a misprint in the latter; the second Jn in the expression for Y(n) should read Jm.)

* Loc. cit. p. 276.