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Angular momentum and Expectation values

  1. Nov 15, 2009 #1
    1. The problem statement, all variables and given/known data

    Express Lx in terms of the commutator of Ly and Lz and, using this result, show that <Lx>=0 for this particle.

    3. The attempt at a solution

    [Ly,Lz]=i(hbar)Lx

    <Lx>=< l,m l Lx l l,m>

    then what?
     
  2. jcsd
  3. Nov 15, 2009 #2
    I can show that <Lx>=0 using the ladder opertators, but i dont think this is what is wanted from this question... how do i use
    [Ly,Lz]=i(hbar)Lx to prove <Lx> = 0?
     
  4. Nov 16, 2009 #3

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    [tex]\langle L_x\rangle=\langle l,m|L_x|l,m\rangle=\frac{-i}{\hbar}\langle l,m|[L_y,L_z]|l,m\rangle[/tex]

    Expand the commutator using its definition, and take the hermitian conjugate of the resulting equation...what do you see?
     
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