# Tag Info

In one of your hang you are already assuming that $P_{ij}|\psi\rangle = |\psi\rangle$, which not true. One way to see that the permutation operator has possible eigenvalues $\pm 1$ is by using that exchanging two identical particles and then exchanging them back should give back the original state, P_{ij}P_{ij}|\psi\rangle = P_{ij}\lambda|\psi\rangle = \...