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On the three-body problem

Published online by Cambridge University Press:  24 October 2008

J. Lekner
J. Lekner
Affiliation:
Cavendish Laboratory, Cambridge
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Abstract

We consider the ground state of a system of three interacting particles of equal mass. An integro-differential equation is obtained for the optimum pair function f in the product wavefunction Ψ(123) = f(12)f(13)f(23). The solution for harmonic forces reproduces the known exact ground state. Approximate analytic solutions are obtained for inverse-square forces, and for a general force law in the semiclassical limit.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 73 , Issue 1 , January 1973 , pp. 177 - 182
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

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