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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.

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