From the equation + 1 = R spatial ( z ^ ^ , 360 ∘ ∘ ) = exp ⁡ ⁡ ( − − 2 π π i L z / ℏ ℏ ) , one picks an eigenstate L z | ψ ψ ⟩ ⟩ = m ℏ ℏ | ψ ψ ⟩ ⟩ and draws e − − 2 π π i m = 1 which is to say that the orbital angular momentum quantum numbers can only be integers, not half-integers.