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Difference in phase convention for Wigner dfunction 
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#1
May314, 11:16 AM

P: 27

I am looking for a way to connect the CondonShortleyWigner to the Edmonds phase convention. Specifically I am writing a program to compute Wignerd matrix coefficients
From tabulated values (e.g. even Wikipedia) d^1/2_{1/2,1/2}=(1)^{1/21/2}d^1/2_{1/2,1/2}=sin(theta/2) So d^1/2_{1/2,1/2}=sin(theta/2) But from Edmonds, eq. 4.1.27 with j=1/2,m=1/2 this should have a  sign e.g. d^j_{mj}=(1)^{jm}[(2j)!/((j+m)!(jm)!]^{1/2} [cos(theta/2)]^{j+m} [sin(theta/2)]^{jm} i.e. j=1/2, m=1/2,j+m=0,jm=1  sqrt(1!/(0! 1!)) [cos(theta/2)]^0 [sin(theta/2)]^1, i.e. the sign is off Is this an Edmonds typo or some different phase convention? 


#2
May614, 11:48 PM

Admin
P: 9,067

I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?



#3
Jun3014, 05:04 AM

P: 27

Yes, Edmonds has a typo. There should be no (1)**(jm) there.



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