What kind of question is it?

roshan2004

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?

Petr Mugver

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.

roshan2004

Pls Can you show it to me how?

Petr Mugver

I can try, but first you have to tell me which is the operator you want to calculate the commutator with parity.

roshan2004

Hermitian operator

Petr Mugver

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...

roshan2004

So, wasn't the question a wrong one?

the_house

If it really implied that the parity operator commutes with all Hermitian operators, then yes, it was wrong.