Prove: Hermitian Operators (QR)*=R*Q*

[Funzies]

Homework Statement

Prove: (QR)*=R*Q*, where Q and R are operators.
(Bij * I mean the hermitian conjugate! I didn't know how to produce that weird hermitian cross)

The Attempt at a Solution

I have to prove this for a quantum physics course, so I use Dirac's notation with two random functions f and g:

<f|(QR)g> = <Q*f|Rg> = <R*Q*f|g>

(Here I have used that Q and R are hermitian operators: <f|Qg>=<Q*f|g> )

I have the answer and it just says that:

<R*Q*f|g>=<(QR)*f|g>

But that means that they've used that the product of two hermitian operators is also hermitian. However, I have proved before that the product of two hermitian operators is only hermitian if the two operators Commutate: [Q,R]=0

Can you explain to me why this holds in this case?

 

[micromass]

I don't see where you used that Q is Hermitian...
To my knowledge, the equation <f|Q*g>=<Qf,g> holds for every operator.
The place where Hermitian comes in, is that Q*=Q...