This places a constraint on the change in total angular momentum. Any state can be rotated so that its angular momentum is in the z -direction as much as possible, where m = ℓ. The matrix element of the position acting on | ℓ, m ⟩ can only produce values of m which are bigger by one unit, so that if the coordinates are rotated so that the final state is | ℓ',ℓ' ⟩, the value of ℓ’ can be at most one bigger than the biggest value of ℓ that occurs in the initial state. So ℓ ’ is at most ℓ + 1.