1. The problem statement, all variables and given/known data Ok, here is another little pickle. I am trying to determine what the eigenfunctions and eigenvalues are for the operator C that is defined such that C phi(x) = phi*(x). Part a wants to know if this is a Hermitian operator. Parts b,c want eigenfunctions and eigenvalues. 2. Relevant equations If an operator is Hermitian, then C=C^t, where ^t is the adjoint symbol. 3. The attempt at a solution From parts b and c and the fact that the section preceding this problem is called "Properties of Hermitian Operators", we might expect C to be Hermitian. BUT - here's what I found: If we assume C is Hermitian, that would mean that < phi| C psi> = <phi | psi*> = [tex]\int[/tex]phi* psi* dx which would have to also equal < C^t phi| psi> = < C phi| psi> = < phi* | psi> = [tex]\int[/tex]phi psi dx and I would argue that in general these two integrals are strictly not the same! This would imply that C is not Hermitian, but if C isn't, then I haven't the foggiest idea how to speculate what the eigenfunctions and eigenvalues are. It seems like there's a mistake and it should be Hermitian so that I can just assert that it has real eigenvalues and orthogonal (normalizable) eigenfunctions. What's the deal?