Wigner3j symbol

Version 1.1.0.0 (2.01 KB) by Kobi
Wigner3j( J123, M123) calculates the Wigner 3j symbol.
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Updated 1 Aug 2013

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Wigner3j( J123, M123) calculates the Wigner 3j-symbol according to Racah formula.
The Wigner 3j symbol is useful for multiplication of Spherical Harmonics (and their generalizations) and for addition of angular momentum.
The are related to the Clebsch-Gordan coefficients by:
Wigner3j( J123, M123 ) = <J1,J2,M1,M2| J1,J2,J3,-M3> * (-1)^(J1-J2-M3) * (2*J3+1)^(-1/2).
This function is not limited to the factorial limitation (170), so it can be useful for any value of J.

Cite As

Kobi (2025). Wigner3j symbol (https://www.mathworks.com/matlabcentral/fileexchange/20619-wigner3j-symbol), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2007b
Compatible with any release
Platform Compatibility
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Inspired by: Wigner3j.m

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Version Published Release Notes
1.1.0.0

(1) Zero value replaces the error massages for the selection rules: m1+m2+m3~=0, j3 > |j1-j2|, j3 > j1+j2, |mi| > ji.
Thanks to Barratt Park and Brice DUBOST.

(2) Warning massages are identified.
1.0.0.0