and let R ^ ^ = R ^ ^ ( θ θ , n ^ ^ ) be a rotation matrix. According to the Rodrigues' rotation formula, the rotation operator then amounts to U [ R ( θ θ , n ^ ^ ) ] = 1 1 − − i sin ⁡ ⁡ θ θ ℏ ℏ n ^ ^ ⋅ ⋅ J − − 1 − − cos ⁡ ⁡ θ θ ℏ ℏ 2 ( n ^ ^ ⋅ ⋅ J ) 2 .