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Wave functions

  1. Jan 29, 2008 #1
    [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


    thank you
  2. jcsd
  3. Jan 30, 2008 #2


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    Start by writing out [itex]\hat L_{z,\mathrm{total}}[/itex] and [itex]\hat S_{z,\mathrm{total}}[/itex].
  4. Jan 30, 2008 #3
    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?
  5. Jan 31, 2008 #4
    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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