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Angular Momentum Operators

  1. Dec 13, 2006 #1
    1. The problem statement, all variables and given/known data
    Show that for the eigenstate |l,m> of L^2 and Lz, the expectation values of Lx^2 and Ly^2 are <Lx^2>=<Ly^2>=1/2*[l(l+1)-m^2]hbar^2

    and for uncertainties, show that deltaLx=deltaLy={1/2*[l(l+1)-m^2]hbar^2}^(0.5)

    2. Relevant equations
    eigenvalues of L^2 are l(l+1)hbar^@
    eigenvalues of Lz are m*hbar


    3. The attempt at a solution
    I noticed that the expectation values are very closely related to the eigenvalues of L^2 and Lz. So I tried using commutator relationships to somehow get Lx^2 as a result.
    [Lz,Lx^2] = ihbar(Lx*Ly+Ly*Lx)
    [Lx,Ly^2] = -ihbar(Lx*Ly+Ly*Lx)
    [L^2,Lx] = [L^2,Ly] = 0
    but none of these seem to help at all......any suggestions on how to approach the problem?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 13, 2006 #2

    Physics Monkey

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    Homework Helper

    Two hints for you azone:

    1) [tex] L^2 = L_z^2+L_x^2 +L_y^2 [\tex]

    2) There is symmetry between x and y
     
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