- #1
Trance
- 11
- 0
Hello everybody, long time reader, first time poster.
I've searched the forums extensively (and what seems like 60% of the entire internet) for anything relevant and haven't found anything, please point me in the right direction if you've seen this before!
Show that even though Q and R are Hermitian operators, QR is only Hermitian if [Q,R]=0
[Q,R] = QR - RQ
[Q,R]* = R*Q*-Q*R*
I've managed to prove, using the definition of Hermiticity that:
∫f(i(QR-RQ))g dτ = ∫g(i(QR-RQ))*f dτ
For two random functions, f and g, and i= Sqrt(-1)
But I'm not sure how relevant this is... I don't have a strong enough intuition to see whether or not this immediately proves anything. Any help would be greatly appreciated!
I've searched the forums extensively (and what seems like 60% of the entire internet) for anything relevant and haven't found anything, please point me in the right direction if you've seen this before!
Homework Statement
Show that even though Q and R are Hermitian operators, QR is only Hermitian if [Q,R]=0
Homework Equations
[Q,R] = QR - RQ
[Q,R]* = R*Q*-Q*R*
The Attempt at a Solution
I've managed to prove, using the definition of Hermiticity that:
∫f(i(QR-RQ))g dτ = ∫g(i(QR-RQ))*f dτ
For two random functions, f and g, and i= Sqrt(-1)
But I'm not sure how relevant this is... I don't have a strong enough intuition to see whether or not this immediately proves anything. Any help would be greatly appreciated!