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Cubic harmonics in Cartesian coordinates
Author(s) -
Kwiatkowski T.,
Olszewski S.,
Wierzbicki A.
Publication year - 1977
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.560110104
Subject(s) - cartesian coordinate system , harmonics , spin weighted spherical harmonics , solid harmonics , spherical harmonics , representation (politics) , point (geometry) , irreducible representation , mathematics , vector spherical harmonics , cartesian product , group (periodic table) , basis (linear algebra) , mathematical analysis , physics , pure mathematics , quantum mechanics , geometry , combinatorics , voltage , politics , political science , law
A full set of harmonics which are at the basis of all irreducible representations of the cubic point group and having order l ⩽ 16 has been calculated in terms of Cartesian coordinates. Due to their complication, former calculations of harmonics in Cartesian coordinates for half of the irreducible representations did not exceed l = 6. The method presented in this paper is a modification of that originally given by Von der Lage and Bethe; it can be readily applied to the calculation of harmonics of arbitrary order for any irreducible representation of the cubic point group.