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Am I crazy, or is there a sign error in the eigenvalue in eq 4.136? As written it is <math> S_\pm \, |s\, m> = \hbar \sqrt{s(s+1) - m(m\pm1)} \, |s \,(m\pm1)> </math>

But when I do

<math>S_{+} \chi_-</math> with this, I get <math>\frac{\hbar}{\sqrt{2}}</math> as the eigenvalue. Shouldn't I get an eigenvalue of <math>\hbar</math> ??
What am I doing wrong?

Oh. Embarrassed. Arithmetic error.

One more picky point. This factor is not an eigenvalue strictly speaking since the vectors on the LHS and RHS are not the same.

Why is it that energy is discrete but linear momentum is not? Aren't they related? I'm having a hard time understanding this.

I've got a question I've been meaning to ask for a while but keep forgetting to post…A while back I was reading through the Angular Momentum chapter again, and came across the part where they're talking about how the Lx, Ly, and Lz commutators go. In equation 4.97, they jump to equation 4.98 while dropping two terms and simplifying the remaining….Now it looks like all they did was pull a y px out of the first term, and an x py out of the second term, even though each is only associated with one of the two terms. Is there some identity that lets you do this, or does it just work out this way by expanding the commutators and doing algebra?

In class today, Yuichi expressed the relations from Clebsch-Gordan table as being a sum of the two possible states (with respective probabilities) as being equal to a third state (of probability one). My question is how did he get the expressions for the components inside of the kets of the third relation. I believe it was |5/2> (maybe 3/2) and

Love,

Esquire

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