< l,m | Lx2 - Ly2 | l,m > = 0
L2 = Lx2 + Ly2 + Lz2
[ Lx, Ly ] = i [STRIKE]h[/STRIKE] Lz
[ L, Lz ] = i [STRIKE]h[/STRIKE] Lx
[ Lz, Lx ] = i [STRIKE]h[/STRIKE] Ly
The Attempt at a Solution
I tried substituting different commutation values in place of Lx and Ly, but I'm not reducing it any further. I also tried ladder operations, but my professor said they're not needed to solve the problem.