Does the Parity Operator Commute with All Hermitian Operators?

  • Thread starter roshan2004
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In summary, the conversation discusses the topic of proving that the parity operation commutes with a Hermitian operator. The speaker wonders how this can be shown, as they only know how to prove that the parity operator is Hermitian. The other speaker explains that the parity operator acts on wave functions with a phase factor, making it easy to prove the commutation relations needed. When asked for an example, the speaker clarifies that the parity operator does not commute with coordinate or momentum operators, but does commute with orbital angular momentum or spin. The conversation ends with the realization that the original question may have been incorrect if it implied that the parity operator commutes with all Hermitian operators.
  • #1
roshan2004
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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?
 
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  • #2
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.
 
  • #3
Pls Can you show it to me how?
 
  • #4
I can try, but first you have to tell me which is the operator you want to calculate the commutator with parity.
 
  • #5
Hermitian operator
 
  • #6
roshan2004 said:
Hermitian operator

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...
 
  • #7
So, wasn't the question a wrong one?
 
  • #8
If it really implied that the parity operator commutes with all Hermitian operators, then yes, it was wrong.
 

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