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LogicX
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Homework Statement
You are given a self-adjoint operator [itex]\hat{A}[/itex] and the equation and [itex]\hat{A}\Phi_{i} ~=~ \Phi_{i}a_{i}[/itex]. Prove that ai are real numbers.
Homework Equations
There are instructions to guide me along with the question. The first step it says to do is write the eigenvalue equation (what I have already written above) and its complex conjugate.
The Attempt at a Solution
I feel like I would have a decent shot of doing this on my own if I could get this first step. I'm not sure what the complex conjugate of an eigenvalue equation looks like. The eigenfunction is [itex]\Phi[/itex]. A hat is an operator, and ai is the eigenvalue. So is the complex conjugate just replacing a with a*? I've tried to look this up online and in my book and I can't find anything.
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