```Date: Jan 26, 2013 10:02 PM
Author: Will Janoschka
Subject: Re: Susskind's proof of orthogonality of eigenvectors

On Sat, 26 Jan 2013 21:01:30, Hetware <hattons@speakyeasy.net> wrote:> http://www.youtube.com/watch?v=CaTF4QZ94Fk&list=ECA27CEA1B8B27EB67> > Lecture 3, beginning around 1:03:20.> > This is what I believe he intended:> > Begin with the assumption that we have two unique eigenvalues for a 2X2 > Hermitian matrix.> > M|a> = lambda_a|a>> > M|b> = lambda_b|b>> > Multiply the first by the conjugate of the second and the second by the > conjugate of the first.> > <b|M|a> = lambda_a<b|a>> > <a|M|b> = lambda_b<a|b>> > Observe that:> > <a|M|b> = <b|M|a>*> > <a|b> = <b|a>*> > So, as I understand it:> > <a|M|b> = lambda_b<a|b> = <b|M|a>* = lambda_b<b|a>*> > Notice this is different from what Susskind presents.  I have not > conjugated lambda_b, whereas he did.  I know he has already stated that > the eigenvalues are real, so lambda_b*=lambda_b.  Therefore, there is no > difference in bedeutung (denotation).  There is a difference in > sinn(sense), however.> > I don't see the motivation for conjugating lambda_b where he did so.  He > isn't really conjugating  both sides of the equation:> > <a|M|b> = lambda_b<a|b>> > That would result in:> > <a|M|b>* = (lambda_b<a|b>)* = <b|M|a> = lambda_b*<b|a>,> > if I'm not mistaken.> > One comment on the YouTube page says that he screwed up the presentation > at that point.  It certainly made me do a double-take, but if he had > said something like "Now we rewrite <a|M|b> = lambda_b<a|b> in it's > equivalent complex conjugate form by replacing all terms by equivalent > complex conjugate terms."  I believe his development would be > procedurally valid.> > Does that make sense?No!      Nor do you!  Complex conjugate in how many terms?Four is not enough!
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