Wave functions

[SOLVED] wave functions

I realize that I have to provide what I have done first for every problem, but this one has stumped be. It is a bonus problem provided by my teacher and it is beyond our scope. thats why its a bonus. Just helping me start it would be a big help. thank you

http://img301.imageshack.us/img301/2531/46008754yl9.jpg [Broken]

thank you

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CompuChip
Homework Helper
Start by writing out $\hat L_{z,\mathrm{total}}$ and $\hat S_{z,\mathrm{total}}$.

here is what I have so far

Sz(total) = Sz1 + Sz2
Sz(alpha) = +(1/2)hbar(alpha)
Sz(beta) = -(1/2)hbar(beta)

Lz(total) = Lz1 + Lz2
Lz(alpha) = + hbar(alpha)
Lz(beta) = - hbar(beta)

Is this correct?
If so, then what?

In the case of spin, use the fact the spin functions only act on states alpha and beta. I.e. write out the determinant, which for a 2x2 matrix is ad-bc, act on $\psi (1,2)$ with $$\hat{S}_{z,total}$$ and then see if you get back an eigenvalue equation.
Also remember that $S_{z,1}, S_{z,2}$ only acts on states 1 and 2 respectively.