1. The problem statement, all variables and given/known data I need to show that < n l m | z | n l m > = 0 for all states | n l m> 2. Relevent Equations: L^2 = Lx^2 + Ly^2 + Lz ^2 Lx = yp(z) - zp(y) Ly = zp(x) - xp(z) Lz = xp(y) - yp(x) L+/- = Lx +/- iLy 3. The attempt at a solution I really don't know where to begin because z is not an eigenfuntion of | n l m> (and if it was this equation would not be 0 anyways). My intuition tells me that I need to somehow represent z as a function of the operators L^2, Lz, and maybe L+/-. But I can't seem to isolate z. Maybe I'm looking at this problem the wrong way. Is there some fundamental theorem that would show that this equation is true?