More generally, consider a linear combination of such states, | Ψ Ψ ⟩ ⟩ . For the best representation of the physical system, we expect this to be an eigenvector of P since exchange operator is not excepted to give completely different vectors in projective Hilbert space. Since P 2 = 1 , the possible eigenvalues of P are +1 and −1. The | Ψ Ψ ⟩ ⟩ states for identical particle system are represented as symmetric for +1 eigenvalue or antisymmetric for -1 eigenvalue as follows: