Stability Configurations of Electrons on a Sphere
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- by Michael Goldberg PDF
- Math. Comp. 23 (1969), 785-786 Request permission
Abstract:
Stable arrangements of electrons in equilibrium on the surface of a sphere have been obtained for most of the cases up to 14 electrons. They resemble the arrangements of the contact points of the faces of an $n$-hedron of least volume circumscribed about the sphere, except for $n = 8$. In this case, it is shown that the electrons near the contact points are in equilibrium, but the arrangement is not stable.References
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L. Föppl, “Stabile Anordnungen von Elektronen im Atom,” J. Reine Angew. Math., v. 141, 1912, pp. 251–301.
- Harvey Cohn, Stability configurations of electrons on a sphere, Math. Tables Aids Comput. 10 (1956), 117–120. MR 81133, DOI 10.1090/S0025-5718-1956-0081133-0 M. Goldberg, “The isoperimetric problem for polyhedra,” Tôhoku Math. J., v. 40, 1935, pp. 226–236.
Additional Information
- © Copyright 1969 American Mathematical Society
- Journal: Math. Comp. 23 (1969), 785-786
- DOI: https://doi.org/10.1090/S0025-5718-69-99642-2