U ( R ) | j , k ⟩ ⟩ = exp ⁡ ⁡ ( − − i θ θ ℏ ℏ n ^ ^ ⋅ ⋅ J → → ) | j , k ⟩ ⟩ = ∑ ∑ j ′ , k ′ | j ′ , k ′ ⟩ ⟩ ⟨ ⟨ j ′ , k ′ | exp ⁡ ⁡ ( − − i θ θ ℏ ℏ n ^ ^ ⋅ ⋅ J → → ) | j , k ⟩ ⟩ = ∑ ∑ k ′ D k ′ k ( j ) ( R ) | j , k ′ ⟩ ⟩