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Translation of real solid spherical harmonics
Author(s) -
Rico Jaime Fernández,
López Rafael,
Ema Ignacio,
Ramírez Guillermo
Publication year - 2012
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.24356
Subject(s) - harmonics , pointwise , solid harmonics , translation (biology) , spherical harmonics , spin weighted spherical harmonics , vector spherical harmonics , range (aeronautics) , zonal spherical harmonics , charge (physics) , physics , mathematical analysis , mathematics , quantum mechanics , chemistry , engineering , aerospace engineering , voltage , biochemistry , messenger rna , gene
General formulae for the translation of both regular and irregular real solid harmonics are derived from the addition theorems of complex harmonics. The resultant expressions, being too complicated for practical purposes, are rewritten in a more compact and friendly manner. The usefulness of these simplified expressions is illustrated with two examples: the potential generated by sets of charges and multipoles in points placed far away, and the expansion in regular harmonics of the long‐range potential inside a region surrounded by pointwise charge distributions. © 2012 Wiley Periodicals, Inc.