Well, the converse of the first one would be: if the eigenfunctions of an operator are complete then the operator is hermitian.
the second would be: if the eigenfunctions of an operator belonging to distinct eigenvalues are orthogonal then the operator is hermitian.
and the third is: If the...
This is really bothering me
I'm remembering from a while ago having to prove the converse of a theorem from Griffiths, but I can't remember which one of the following it is:
Prove converse of:
1.) The eigenfunctions of a Hermitian operator are complete,
2.) Eigenfunctions of Hermitian...
I'm looking for a proof of the fact that orthogonal eigenfunctions of a Hermitian operator have distinct eigenvalues. I know the proof the converse: that eigenfunctions belonging to distinct eigenvalues are orthogonal.
thanks alot!