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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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