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

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Physics

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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