In quantum mechanics, the intrinsic parity is a phase factor that arises as an eigenvalue of the parity operation x i → → x i ′ = − − x i (a reflection about the origin). To see that the parity's eigenvalues are phase factors, we assume an eigenstate of the parity operation (this is realized because the intrinsic parity is a property of a particle species) and use the fact that two parity transformations leave the particle in the same state, thus the new wave function can differ by only a phase factor, i.e.: P 2 ψ ψ = e i ϕ ϕ ψ ψ thus P ψ ψ = ± ± e i ϕ ϕ / 2 ψ ψ , since these are the only eigenstates satisfying the above equation.