I Coupling 3 spin 1/2 particles

  • Thread starter JoJoQuinoa
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Hello,

I'm trying to couple 3 spin 1/2 particles. So far, I have been able to find the coefficient for the other states but I can't get the results for ##j_{12} = 0## to ##j_3=1/2##.
Here is my attempt:
1) Using CG table ##<j_1;j_2;m_1;m_2|J;M><\frac{1}{2};\frac{1}{2};-\frac{1}{2};\frac{1}{2}|0;0> = 1/\sqrt2##
2) Using CG table again with ##\frac{1}{\sqrt2}<0;\frac{1}{2};0;\frac{1}{2}|\frac{1}{2};\frac{1}{2}> = 1/\sqrt2*1/\sqrt3 = 1/\sqrt6##

The correct answer is ##1/\sqrt2##.

Please help!

Thank you
 

Meir Achuz

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Your second C-G is wrong. Adding L=0 to anything has C-G=1.
 
Your second C-G is wrong. Adding L=0 to anything has C-G=1.
Hi Meir Achuz,

Thank you for your reply. Do you mind explaining a little bit in details or direct me to where I can find more info on that? The sources I've looked at only listed the results so I guess this is supposed to be known? I'm using Quantum Mechanics by David H. McIntyre.
 

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