The parity operator P is defined by
ˆ Pψ (x) =ψ (−x)
for any function ψ(x).
(a) Prove that this parity operator P is Hermitian.
(b) Find its eigenvalues, and also its eigenfunctions (in termsof ψ(x)).
(c) Prove that this parity operator commutes with theHamiltonian when potential V(x) is an even function.
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