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Complementary variational principles for ∇2φ = f(φ) with applications to the Thomas–Fermi and Liouville equations

Published online by Cambridge University Press:  24 October 2008

A. M. Arthurs  and
P. D. Robinson
A. M. Arthurs
Affiliation:
University of York
P. D. Robinson
Affiliation:
University of York
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Abstract

Complementary variational principles associated with the boundary-value problem ∇2φ = f(φ) in ∇,φ = φ0 on the boundary of ∇, are presented. The theory is applied to the Thomas–Fermi equation in quantum mechanics and the Liouville equation in equilibrium statistical mechanics.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 2 , March 1969 , pp. 535 - 541
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

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