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Homework Help: Total angular momentum OP

  1. Oct 17, 2012 #1
    HI,i am aiming to show that 1/(2)^1/2(|spin up>|spin down> + |spin down>|spin up>) is an eigenvalue to the total angular momentum operator in a two-electron system.


    I know that i should end up with getting the eigenvalues of the separate spins; L1|spin up> and
    L2|spin down> and so on..also i have been suggested to use L+ and L- operators...anyone who can help how to start with the solution? thx a lot!

    Do they mean the total angular momentum to be J=L+s OR L1 + L2??
     
  2. jcsd
  3. Oct 18, 2012 #2
    I think the operator in question would be
    [tex]S^2 = ({\bf S_1} + {\bf S_2})^2.[/tex]
    Try operating on your state with that. You'll need to express the crossterm in terms of ladder operators.
     
  4. Oct 18, 2012 #3
    Thanks. But wouldnt the total angular momentum operator be like, L or J? I mean, not the total spin operator?


    kind regards
     
  5. Oct 18, 2012 #4
    I think when they say "total" here, they're talking about the total spin angular momentum S1 + S2. Not the spin angular momentum plus the orbital angular momentum.
     
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