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Basic commutator of angular momentum

  1. Feb 22, 2015 #1
    Could someone explain to me how the author goes from 2nd to 3rd step

    I think the intermediate step between 2 and 3 is basically to split up the commutator as

    [y p_z, z p_x] - [y p_z,x p_z] - [z p_y,z p_x] + [z p_y, x p_z]

    2nd term = 0
    3rd term = 0

    so leftover is
    [L_x, L_y] = [y p_z, z p_x] + [z p_y, x p_z]

    but how does this turn into what he has on 3rd step?
  2. jcsd
  3. Feb 22, 2015 #2


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    Multiple applications of the Leibniz product rule: ##[AB,C] = A[B,C] + [A,C]B##
  4. Feb 22, 2015 #3
    really? I thought it would be much simpler than that. I thought i was missing a trivial trick.
  5. Feb 22, 2015 #4


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    Once you become proficient with the Leibniz rule, you'll be able to skip steps. E.g., the ##y## in the 1st commutator commutes with ##zp_x##, so it can just be taken out the front, and so on. You could call that a "trivial" trick, but it's wise to carefully practice the Leibniz rule a few times initially, since it's essential when simplifying more difficult commutators.
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