The 5 Electron Case of Thomson's Problem

Details The 5 Electron Case of Thomson's Problem The 5 Electron Case of Thomson's Problem

2010-01-21

arxiv.org/abs/1001.3702v5

Mathematics

Metric Geometry

67 pages, rigorous computer-assisted proof. This and other replacements have fixed various typos

Scientific paper

We give a rigorous computer-assisted proof that the triangular bi-pyramid is the unique configuration of 5 points on the 2-sphere that globally minimizes the Coulomb (1/r) potential. We also prove the same result for the (1/r^2) potential. The main mathematical contribution of the paper is a fairly efficient energy estimate that works for any number of points and any power-law potential.

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