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Homework Help: Angular Momentum Operator

  1. Mar 8, 2010 #1
    The operators used for the x and y components of angular momentum are:

    7B%5Cpartial%7D%7B%5Cpartial%7Bz%7D%7D%20%20-%20z%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial%7By%7D%7D).jpg

    7B%5Cpartial%7D%7B%5Cpartial%7Bx%7D%7D%20%20-%20x%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial%7Bz%7D%7D).jpg

    Show that Lx and Lz obey an uncertainty relation




    2. No relevant equations.




    3. The attempt at a solution

    I'm going on that the assumption that if LxLy - LyLz does not equal zero then they don't commute and have an uncertainty relation. However I can only get this equal to zero and don't know how to show the uncertainty rrelation if I achieve one.
     
  2. jcsd
  3. Mar 8, 2010 #2
    if you mean:

    [Lx, Ly] = LxLy - LyLx

    then it does not equal to zero, angular moment is the cross product: r x p

    so Lx = y.Pz - z.Py Ly = x.Pz - z.Px

    where x and y and z are position operators and Px, Py and Pz are momentum operators, stick those into your commutator and try again, you should end up with

    [Lx, Ly] = ihLz

    where h is the reduced planck constant. and Lz is the Angular momentum operator for z axis
     
  4. Mar 8, 2010 #3

    vela

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    It would also help if you showed us your calculation of the commutator so we can see where your error is.
     
  5. Mar 15, 2010 #4
    Ah I got it solved in the end. Just made a minor mistake. Thanks!
     
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