When solving to find eigenstates of the operator L 2 , we obtain the following L 2 | ℓ ℓ , m ⟩ = ℏ ℏ 2 ℓ ℓ ( ℓ ℓ + 1 ) | ℓ ℓ , m ⟩ L z | ℓ ℓ , m ⟩ = ℏ ℏ m | ℓ ℓ , m ⟩ where ⟨ θ θ , ϕ ϕ | ℓ ℓ , m ⟩ = Y ℓ ℓ , m ( θ θ , ϕ ϕ ) are the spherical harmonics.