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Homework Statement
In the calculation of the Zeeman Effect, the most important calculation is
[tex]\langle L_z + 2S_z \rangle = \langle J_z + S_z\rangle[/tex]
Suppose we want to find the Zeeman Effect for ##(2p)^2##, meaning ##l=1##.
In Sakurai's book,
My question is, what is ##m##? They say that ##m## is the eigenvalue of ##J_z##, meaning ##J_z = l + m_s = \frac{3}{2}## in this case.
Homework Equations
The Attempt at a Solution
Using ##m = \frac{3}{2}##, it gives the wrong Gordon-Clebsch coefficients.
I have worked out the correct form, which is adding orbital angular momentum ##(l=1)## to its spin ##(\pm\frac{1}{2})##
[tex]|l + s, m_l + m_s\rangle = |\frac{3}{2},\frac{1}{2}\rangle = \sqrt{\frac{1}{3}}|1,1\rangle|-\rangle + \sqrt{\frac{2}{3}}|1,0\rangle|+\rangle[/tex]
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