If $\displaystyle V(-x) = V(x)$, prove $\displaystyle [H,P] = 0$, where $\displaystyle H$ is the hamiltonian operator and $\displaystyle P$ is the parity operator.

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We know that this is an even function (so even parity..) and has behavior like cosine. Not sure how to prove this- maybe using the general $\displaystyle HP - PH$ idea?