Hermitian Operators Question

  • #1
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Homework Statement


[A,B] = C and operators A,B,C are all hermitian show that C=0


Homework Equations





The Attempt at a Solution



Since it is given that all operators are hermitian I know that A=A' B=B' and C=C' so i expanded it out to
AB-BA=C
A'B'-B'A'=C
(BA)' - (AB)'=C


I'm not real sure where I am supposed to go or what properties of hermitian operators I am supposed to used to show that AB=BA..any help would be appreciated thank
 
  • #2
Going back to AB-BA=C, what is C' equal to? How does it compare to what you derived so far?
 
  • #3
Going back to AB-BA=C, what is C' equal to? How does it compare to what you derived so far?

So would I just treat C and C' as separate equations, equate them and show that it equals zero?

ie:

C'=AB-BA
C=(BA)'-(AB)' and just use the fact that all the operators are hermitian?
 
  • #4
Not exactly. You have C=AB-BA, so C' = (AB-BA)'. With a little algebra, you should be able to show that C' = -C.
 

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