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Wigner3j symbol

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Wigner3j symbol

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09 Jul 2008 (Updated )

Wigner3j( J123, M123) calculates the Wigner 3j symbol.

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Description

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.

Acknowledgements

Wigner3j.M inspired this file.

MATLAB release MATLAB 7.5 (R2007b)
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Comments and Ratings (3)
09 Sep 2009 Barratt Park

Instead of returning zero when the triangle rule abs(j1-j2)<=j3<=(j1+j2) or the projection addition rule m1+m2=m3, this program instead returns an error message. In my opinion this is not how a Three-J script should work, since many programers will want to apply a Three-J even in cases where it is trivially zero. The script should be modified to return zero when the Three-J is trivially equal to zero.

05 Nov 2008 Brice DUBOST

Please replace "m3 does not match m1 + m2" and the triangle condition by returning 0 instead of an error message

11 Aug 2008 Bruno Masiero

On line 35, to the check if m1+m2 = m3, you should use:

m1 + m2 - m3 ~= 0

cheers

Updates
01 Aug 2013

(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.

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