# 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?

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Hints:

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.

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Thank you, Qmechanic. –  D. Harris Nov 19 '12 at 19:20