On Sat, 26 Jan 2013 21:01:30, Hetware <firstname.lastname@example.org> 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!