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Commutation of Angular and Linear Momentum

  1. Oct 17, 2011 #1
    If I have a relation such as [tex][L_{j} , \vec{p}^2]=0[/tex] where j=x,y,z.

    Can I re-write it as [tex][L_{j}, \vec{p} \vec{p}]=0[/tex] and then evaluate it as though it were an identity? e.g. [tex][A,BC]=[A,B]C+[B,A]C=...[/tex]
  2. jcsd
  3. Oct 17, 2011 #2
    If unsure, you are better off explicitly writing out the dot product:
    [itex][ L_j, \vec{p}^2] = [L_j, \sum_{k} p_k^2] = \sum_{k} [L_j, p_k^2][/itex]

    Now you can apply the ABC rule. The one you quote is wrong, by the way. It should be:
    [itex][A, BC] = B[A,C] + [A,B]C[/itex]
  4. Oct 18, 2011 #3
    Thanks for the help!
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