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FlagellumDei

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## Homework Statement

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?

## Homework Equations

If C is hermitian, then <C(psi1)\(psi2)>=<(psi1)\C(psi2)>

For eigenvalues: C(psi)=a(psi), where a is a constant

## 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?

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