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In: Physics

The parity operator P is defined by ˆ Pψ (x) =ψ (−x) for any function ψ(x)....

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 terms of ψ(x)).

(c) Prove that this parity operator commutes with the Hamiltonian when potential V(x) is an even function.

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