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Ed Quanta
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Homework Statement
Show that the eigenvectors of a unitary transformation belonging to distinct eigenvalues are orthogonal.
Homework Equations
I know that U+=U^-1 (U dagger = U inverse)
The Attempt at a Solution
I tried using a similar method to the proof which shows that the eigenvectors of hermitian transformations belonging to distinct eigenvalues are orthogonal.
So assume our eigenvectors are a and b. I assumed U(a)=xa and U(b)=yb
x<a|b>=<Ua|b>=<a|U^-1b>= ?
Help anyone. I know this probably isn't too rough.