Parity operator
= Parity operator
{title2=$P$}
The parity operator acts on a spatial <wavefunction> by $(P\psi)(x)=\psi(-x)$ and satisfies $P^2=I$. For a <Hamiltonian operator> with an even potential and parity-invariant domain, $HP=PH$. A <nondegenerate energy eigenvalue> has a one-dimensional <eigenspace>, so its eigenfunction is an eigenvector of $P$ with eigenvalue $+1$ or $-1$.