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Notes on the two-centre problem in wave mechanics

II. Some new solutions of the wave equation

Published online by Cambridge University Press:  24 October 2008

P. E. Marrack
P. E. Marrack
Affiliation:
The AdmiraltyLondon
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Extract

The paper deals with new solutions of the differential equations of the two-centre problem which are expressed in terms of the confluent hypergeometric function. By means of this function a solution of the λ-equation (1) is obtained which enables the separation constant A to be found for small values of the parameter p in a rapidly convergent series, which for the special case of m = 0 is still more rapidly convergent. The solution for the μ-equation (2) in the general case is of the same character as regards rapidity of convergence as solutions previously obtained, but when m = 0 it again possesses a higher rate of convergence as compared with solutions given by other investigators.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 37 , Issue 4 , October 1941 , pp. 384 - 396
Copyright
Copyright © Cambridge Philosophical Society 1941

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References

* Baber, and Hassé, , Proc. Cambridge Phil. Soc. 31 (1935), 564CrossRefGoogle Scholar. Marrack, , Proc. Cambridge Phil. Soc. 35 (1939), 44.CrossRefGoogle Scholar