The Five-Electron Case of Thomson's Problem

被引：40
作者：
Schwartz, Richard Evan [1 ]
机构：
[1] Brown Univ, Dept Math, Providence, RI 02912 USA
来源：
EXPERIMENTAL MATHEMATICS | 2013年 / 22卷 / 02期
基金：
美国国家科学基金会;
关键词：
51-04; 51F99; 5-electron problem; power-law potential; triangular bi-pyramid; electron configurations; POINTS;
D O I：
10.1080/10586458.2013.766570
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give a rigorous computer-assisted proof that the triangular bipyramid is the unique configuration of five points on the 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.
引用
收藏
页码：157 / 186
页数：30
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