Register to reply

Difference in phase convention for Wigner d-function

by chafelix
Tags: convention, dfunction, difference, phase, wigner
Share this thread:
May3-14, 11:16 AM
P: 27
I am looking for a way to connect the Condon-Shortley-Wigner to the Edmonds phase convention. Specifically I am writing a program to compute Wigner-d matrix coefficients

From tabulated values (e.g. even Wikipedia) d^1/2_{1/2,-1/2}=(-1)^{-1/2-1/2}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
d^j_{mj}=(-1)^{j-m}[(2j)!/((j+m)!(j-m)!]^{1/2} [cos(theta/2)]^{j+m} [sin(theta/2)]^{j-m}

i.e. j=1/2, m=-1/2,j+m=0,j-m=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?
Phys.Org News Partner Physics news on
Organic photovoltaic cells of the future: Charge formation efficiency used to screen materials
Promising ferroelectric materials suffer from unexpected electric polarizations
Structure of certain types of beetle shells could inspire brighter, whiter coatings and materials
Greg Bernhardt
May6-14, 11:48 PM
Greg Bernhardt's Avatar
P: 9,489
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?
Jun30-14, 05:04 AM
P: 27
Yes, Edmonds has a typo. There should be no (-1)**(j-m) there.

Register to reply

Related Discussions
Is the wigner D function a representation of SO(3)? Quantum Physics 1
Wigner distribution in phase space Quantum Physics 3
Phase, Phase Difference and Phase Shift General Physics 6
Phase Displacement Convention Engineering, Comp Sci, & Technology Homework 0
What is the physical significance of phase or phase difference General Physics 3