1. The problem statement, all variables and given/known data C is an operator that changes a function to its complex conjugate a) Determine whether C is hermitian or not b) Find the eigenvalues of C c) Determine if eigenfunctions form a complete set and have orthogonality. d) Why is the expected value of a squared hermitian operator always positive? 2. Relevant equations If C is hermitian, then <C(psi1)\(psi2)>=<(psi1)\C(psi2)> For eigenvalues: C(psi)=a(psi), where a is a constant 3. The attempt at a solution I don't know even if I'm doing wrong but using the condition for hermiticity described above I get the integrals for the products (psi*)(psi*) and (psi)(psi) are equal. (Being the terms with "*" the complex conjugate) For d), if the operator is squared, then the constant is squared too, but how do I know "a" is not a complex constant? Ok, I guess I was a little desperate ad didn't check my results as I had to, from the beggining. Simply substituting C(psi) for (psi*) and (psi*) for C(psi) makes evident C is hermitian. Then, there's a theorem stating eigenvalues of hermitian operators are real, because average values are always real numbers. Squaring the constant makes for a positive number. Yet I'm not sure how to get the eigenvalues of b). How "far" can I go with this information?