Show that the expectation value of angular momentum <Lx> is zero
L±|l,m⟩ = SQRT(l(l+1)−m(m±1)h|l,m±1⟩
L± = Lx ± iLy
The Attempt at a Solution
I'm supposed to use ladder operators here to show <Lx> is zero.
I start with <Lx>=<l,m|Lx|l,m> but don't know where to go from here. I've tried different things but all the methods I've tried seem to lead to a dead end...