(adsbygoogle = window.adsbygoogle || []).push({}); 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

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# Angular Momentum Operators

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