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Notes on the two-centre problem in wave mechanics. I. The hyperbolic nodes of the wave equation

Published online by Cambridge University Press:  24 October 2008

P. E. Marrack
P. E. Marrack
Affiliation:
The Admiralty, London
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Extract

Approximate expressions are obtained, when the distance R between the nuclei is very large, for that portion of the wave function in the two-centre problem which depends on the hyperbolic coordinate μ. From these expressions the number and the approximate position of the nodes in μ can be deduced and hence the rules can be found by which that state of the combined atom at R = 0 can be determined which corresponds to a given state of the atom when the nuclei are completely separated. These rules are also applicable to the cases where the two atoms which can be formed when the nuclei are completely separated have the same energy. The converse problem of finding what state of the completely separated atom corresponds to a given state of the combined atom at R = 0 can also be solved by the use of the rules.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 35 , Issue 1 , January 1939 , pp. 44 - 55
Copyright
Copyright © Cambridge Philosophical Society 1939

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References

* This problem has just recently been considered from a different point of view, which leads to the same conclusions, by MissMonroe, E., Proc. Cambridge Phil. Soc. 34 (1938), 375.CrossRefGoogle Scholar

† Baber, and Hassé, , Proc. Cambridge Phil. Soc. 31 (1935), 564.CrossRefGoogle Scholar

* Airey, and Webb, , Phil. Mag. 36 (1918), 129.CrossRefGoogle Scholar

* Bromwich, , Infinite series, 2nd ed. (London, 1924), p. 341.Google Scholar