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Tensor product: commutator for spin

  1. May 20, 2013 #1
    1. The problem statement, all variables and given/known data

    [S2 total, Sz ∅1]


    2. Relevant equations

    S2 total = S2∅1+ 1∅S2+2(Sx∅Sx+Sy∅Sy+ Sz∅Sz)


    3. The attempt at a solution
    I calculated it in steps:
    (1∅Sx 2 +Sx 2∅1) * Sz ∅1
    =[S2x, Sz] ∅1 + Sz∅Sx 2
    =-h_cut i (SxSy+SySx)∅1 + Sz∅Sx 2

    Is it correct way of doing it? I mean I just did one small segment of it. There is still a lot of calculation to be done. Is there any short method?
     
  2. jcsd
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