An operator Ω Ω ^ ^ is invariant under a unitary transformation U if Ω Ω ^ ^ = U † † Ω Ω ^ ^ U ; in this case for the rotation U ^ ^ ( R ) , Ω Ω ^ ^ = U ( R ) † † Ω Ω ^ ^ U ( R ) = exp ⁡ ⁡ ( i θ θ ℏ ℏ n ^ ^ ⋅ ⋅ J ) Ω Ω ^ ^ exp ⁡ ⁡ ( − − i θ θ ℏ ℏ n ^ ^ ⋅ ⋅ J ) .