Hostname: page-component-7bb8b95d7b-w7rtg Total loading time: 0 Render date: 2024-09-29T17:36:20.176Z Has data issue: false hasContentIssue false
  • English
  • Français

On the three-body problem

Published online by Cambridge University Press:  24 October 2008

J. Lekner
J. Lekner
Affiliation:
Cavendish Laboratory, Cambridge
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Lekner, J.Proc. Cambridge Philos. Soc. 71 (1972), 575.CrossRefGoogle Scholar
(2)Blatt, J. M. and Weisskopf, V. F.Theoretical nuclear physics, Chapter V (John Wiley, 1952).Google Scholar
(3)Noyes, H. P.Prog. Nuclear Phys. 10 (1969), 357.Google Scholar
(4)Amado, R. D.Ann. Rev. Nuclear Sci. 19 (1969), 61.CrossRefGoogle Scholar
(5)Delves, L. M. and Phillips, A. C.Rev. Modern Phys. 41 (1969), 497.CrossRefGoogle Scholar
(6)Schmid, E. W., Schwager, J., Tang, Y. C. and Herndon, R. C.Physica 31 (1965), 1143.CrossRefGoogle Scholar
(7)Stenschke, H. J.Chem. Phys. 53 (1970), 466.Google Scholar
(8)Etters, R. D., Raich, J. C. and Chand, P.J. Chem. Phys. 55 (1971), 5130.CrossRefGoogle Scholar
(9)Green, H. S.Nuclear Phys. 54 (1964), 505.CrossRefGoogle Scholar
(10)Lim, T. K.Nuclear Phys. A139 (1969), 149.CrossRefGoogle Scholar