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Uncertainties & Total Angular Momentum

  1. Jan 16, 2013 #1
    Hey,

    My question is on determining an 'uncertainty' quantity using total angular momentum operators in the x,y and z directions where we know the commutation relations between the x,y and z directions of the total angular momentum operators.

    Uncertainty_Q.png

    I'm not really sure where to go with this at all, I let the commutator given act on a state |m> i.e. an eigenfunction of J(z)

    [tex][\hat{J_{x}},\hat{J_{y}}]|m>=i\hbar\hat{J_{z}}|n>=i\hbar m|m>[/tex]

    So the commutator must equal i*hbar*m, right? Anyway I'm not sure if this is even a correct way to begin, but it should be pretty straightforward however I haven't really come across a question like this before.

    By the way I replaced subscripts 1,2,3 with x,y and z repsectively.

    Thanks for any help!
    SK
     
  2. jcsd
  3. Jan 17, 2013 #2
    Woops, the equation should read:

    not 'n' ket but 'm' ket.

    Sorry...

    SK
     
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