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The objective of the Thomson problem is to determine the minimum electrostatic potential energy configuration of ''N'' electrons on the surface of a unit sphere that repel each other with a force given by Coulomb's law. The physicist J. J. Thomson posed the problem in 1904〔J. J. Thomson, "On the Structure of the Atom: an Investigation of the Stability and Periods of Oscillation of a number of Corpuscles arranged at equal intervals around the Circumference of a Circle; with Application of the Results to the Theory of Atomic Structure", ''Philosophical Magazine'' Series 6, Volume 7, Number 39, pp. 237–265, March 1904. ()〕 after proposing an atomic model, later called the plum pudding model, based on his knowledge of the existence of negatively charged electrons within neutrally-charged atoms. Related problems include the study of the geometry of the minimum energy configuration and the study of the large ''N'' behavior of the minimum energy. == Mathematical statement == The physical system embodied by the Thomson problem is a special case of one of eighteen unsolved mathematics problems proposed by the mathematician Steve Smale — "Distribution of points on the 2-sphere".〔 〕 The solution of each ''N''-electron problem is obtained when the ''N''-electron configuration constrained to the surface of a sphere of unit radius, , yields a global electrostatic potential energy minimum, . The electrostatic interaction energy occurring between each pair of electrons of equal charges (, with the elementary charge of an electron) is given by Coulomb's Law, : is the distance between each pair of electrons located at points on the sphere defined by vectors and , respectively. Simplified units of and are used without loss of generality. Then, :. The global minimization of over all possible collections of ''N'' distinct points is typically found by numerical minimization algorithms. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Thomson problem」の詳細全文を読む スポンサード リンク
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