Can You Help Me Couple 3 Spin 1/2 Particles?

[JoJoQuinoa]

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]

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

 

[JoJoQuinoa]

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.

 

[Meir Achuz]

https://amazon.com/s?k=rose+angular+momentum&ref=nb_sb_noss&tag=pfamazon01-20
is still the best and simplest.