We have a hermitian operator Q and a complex number z. I have an inner product given by:
<f | (zQ) g>,
where f and g are two arbitrary functions. Now taking the hermitian conjugate of a complex number is just taking the complex conjugate of that number. So taking the hermitian conjugate of the above gives me:
<(zQ)H f | g> = <z*QH f | g> = z<QH f | g> = z<Qf | g>
According to my book, this is wrong, because I should end up with z* in front of the inner product, and not z. Where is my reasoning wrong?
Thanks in advance.