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## Homework Statement

Consider the Hamiltonian

[tex]H=\alpha L \cdot S[/tex]

Where L denotes an angular momentum with quantum number l and S a spin with quantum number s.

Work out

[tex]L \cdot S |(ls)jj_{z}>[/tex]

direction. Hint: expand (L+S)

^{2}and go from there.

**2. The attempt at a solution**

I'm highly tempted to start with

[tex]L \cdot S |(ls)jj_{z}> = \frac{\hbar^{2}}{2}[j(j+1)-l(l+1)-3/4]|(ls)jj_{z}>[/tex]

except I'm not sure that really buys me much. If I'm on the right track, how do I then handle the ket?