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Commutation of squared angular momentum operators

  1. Jan 26, 2015 #1
    Hello there. I am trying to proove in a general way that

    [Lx2,Lz2]=[Ly2,Lz2]=[Lz2,Lx2]

    But I am a little bit stuck. I've tried to apply the commutator algebra but I'm not geting very far, and by any means near of a general proof. Any help would be greatly appreciated.

    Thank you.
     
  2. jcsd
  3. Jan 26, 2015 #2

    kith

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    Science Advisor

    Hint: [itex]L^2 = L_x^2 + L_y^2 + L_z^2[/itex]
     
  4. Jan 26, 2015 #3
    Of course! We can show ## [L^2,L_i^2]=0 ## for ## i \in \{x,y,z\} ##

    so

    ## [L_x^2,L_i^2]+[L_y^2,L_i^2]+[L_z^2,L_i^2]=0 ##, and for ## i=z ## and ## i=x## we have the equalities.

    Thank you very much for the hint, I should have seen that sooner
     
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