Angular Momentum Operators

azone

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

Related Advanced Physics Homework News on Phys.org

Physics Monkey

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

"Angular Momentum Operators"

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving