Wave functions

  • Thread starter gazepdapi1
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  • #1
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[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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Answers and Replies

  • #2
CompuChip
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Start by writing out [itex]\hat L_{z,\mathrm{total}}[/itex] and [itex]\hat S_{z,\mathrm{total}}[/itex].
 
  • #3
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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?
 
  • #4
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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 [itex] \psi (1,2) [/itex] with [tex] \hat{S}_{z,total}[/tex] and then see if you get back an eigenvalue equation.
Also remember that [itex] S_{z,1}, S_{z,2} [/itex] only acts on states 1 and 2 respectively.
 

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