1. The problem statement, all variables and given/known data Show that < l,m | Lx2 - Ly2 | l,m > = 0 2. Relevant equations 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 3. 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.