The 5 Electron Case of Thomson's Problem
Metric Geometry
2010-02-08 v5 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.1001.3702,
title = {The 5 Electron Case of Thomson's Problem},
author = {Richard Evan Schwartz},
journal= {arXiv preprint arXiv:1001.3702},
year = {2010}
}
Comments
67 pages, rigorous computer-assisted proof. This and other replacements have fixed various typos