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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.