In my terminal exam I was asked to prove it that the parity operation commutes with Hermitian operator? I wonder how can we show that? coz we can only show that the parity operator is hermitian? We haven't got the value of hermitian operator at all?
On wave functions the parity operator acts something like [tex]P\psi(x)=\eta\psi(-x)[/tex] where \eta is a phase factor independent of x. Now it should be easy to prove all the commutation relations you need.
I can try, but first you have to tell me which is the operator you want to calculate the commutator with parity.
It's not enough. For example, P does not commute with the coordinates x or the momenta p (these anticommute with parity), but it commutes with orbital agular momentum or spin...
If it really implied that the parity operator commutes with all Hermitian operators, then yes, it was wrong.