Although one might expect R ( n ^ ^ , 360 ∘ ∘ ) = 1 (a rotation of 360° is the identity operator), this is not assumed in quantum mechanics, and it turns out it is often not true: When the total angular momentum quantum number is a half-integer (1/2, 3/2, etc.), R ( n ^ ^ , 360 ∘ ∘ ) = − − 1 , and when it is an integer, R ( n ^ ^ , 360 ∘ ∘ ) = + 1 . Mathematically, the structure of rotations in the universe is not SO(3), the group of three-dimensional rotations in classical mechanics. Instead, it is SU(2), which is identical to SO(3) for small rotations, but where a 360° rotation is mathematically distinguished from a rotation of 0°. (A rotation of 720° is, however, the same as a rotation of 0°.)