- #1
azone
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Homework Statement
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)
Homework Equations
eigenvalues of L^2 are l(l+1)hbar^@
eigenvalues of Lz are m*hbar
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?