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Convergence of the bipolar expansion for the coulomb potential
Author(s) -
Silverstone Harris J.
Publication year - 2014
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.24630
Subject(s) - multipole expansion , convergence (economics) , coulomb , series (stratigraphy) , series expansion , charge (physics) , moment (physics) , physics , order (exchange) , electric potential , spherical multipole moments , taylor series , classical mechanics , mathematics , quantum electrodynamics , mathematical analysis , quantum mechanics , fast multipole method , voltage , geology , economics , paleontology , finance , economic growth , electron
The bipolar expansion of the Coulomb potential, which underlies the multipole moment expansion for interacting charge distributions, converges like a geometric series for separated charges, but converges at best only conditionally when the charges interpenetrate. This article shows how the order of summation affects the sum. Evidence is presented for simpler series when the geometry is linear. © 2014 Wiley Periodicals, Inc.