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QM: Spin -orbit coupling: Solve [(L.S), L]

  1. Jan 25, 2008 #1
    [SOLVED] QM: Spin -orbit coupling: Solve [(L.S), L]

    1. The problem statement, all variables and given/known data
    Griffiths problem 6.16
    Solve the following commutators (he lists a bunch but i can't get even the first one)

    (a) [(L.S) , L]
    (b) [(L.S) , S]
    (c) [(L.S) , L^2]

    there's a few more, but i think if i get the idea then i can do the rest. I know it isn't supposed to be hard but for some reason i can't get it.

    Thank you any help you can give.
  2. jcsd
  3. Jan 25, 2008 #2
    The only thing you have to know is the commutators

    [tex][L_i,L_j]=\epsilon_{ijk}\,L_k \quad [L_i,S_j]=0[/tex]

    and the general rule

    [tex] [A\,B,C]=A\,[B,C]+[A,C]\,B[/tex]
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