# Implications of rotational invariance

The state

$$|\psi\rangle ={1\over \sqrt 2}(|+\rangle|-\rangle-|-\rangle|+\rangle)$$

of system made up of 2 spin-$1\over 2$ particles is invariant under the operator

$$\exp{i\theta S_y}.$$

What implications/relations does this have relating to the angular momentum properties of the system?

-

1. Check that the state $|\psi\rangle$ is annihilated by $J_x$, $J_y$, and $J_z$.
2. Deduce that the state $|\psi\rangle$ has zero total angular momentum.