Open AccessAn alternative to Wigner d-matrices for rotating real spherical harmonics
Author(s) -
G. Aubert
Publication year - 2013
Publication title -
aip advances
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.421
H-Index - 58
ISSN - 2158-3226
DOI - 10.1063/1.4811853
Subject(s) - spin weighted spherical harmonics , solid harmonics , spherical harmonics , zonal spherical harmonics , harmonics , rotation (mathematics) , vector spherical harmonics , matrix (chemical analysis) , rotation matrix , transformation (genetics) , tensor operator , transformation matrix , classical mechanics , work (physics) , physics , mathematics , mathematical analysis , geometry , quantum mechanics , chemistry , biochemistry , kinematics , chromatography , voltage , gene
Transformation of spherical harmonics under rotation is a major problem in many areas of theoretical and applied science. While elegantly and efficiently solved for complex spherical harmonics with Wigner D- and d-matrices, extending this method to real spherical harmonics (RSH) faces serious difficulties not yet overcome. This work presents novel explicit formulas and recurrence relations for building RSH rotation matrices with lesser complexity and better computational efficiency. It also gives general closed forms of Wigner d-matrix elements in terms of the rotation angle instead of half this angle as is usual