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I have been looking at the proof that the parity operator is hermitian in 3-D in the QM book by Zettili and I am confused by the following step

∫ d^{3}r φ*(r)ψ(-r) =∫ d^{3}r φ*(-r)ψ(r)

I realise that the variable has been changed fromrto -r. In 3-D x,y,z this is achieved by taking the modulus of the Jacobian which obviously gives a positive value as opposed to working in I-D when a minus sign arises. But on the LHS of the equation the triple integrals all had +∞ at the top and -∞ at the bottom but on the RHS changing the variable results in -∞ at the top of the integrals and +∞ at the bottom. Is this correct ?

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# I Proof that parity operator is Hermitian in 3-D

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