---- for character building: If you want to work through my presentation of group theoretical projection operators, the method is in the appendix A of http://www.cns.gatech.edu/FieldTheory/QMlectures/lectQM.pdf (text identical to the version posted in January), or in Sect 3.6 of ChaosBook.org/GroupTheory ---- curiosity: Interestingly enough, a former professor at Georgia Tech wrote identical appendix (!) independently of myself in W.~G.~Harter and N.~Dos Santos, ``Double-group theory on the half-shell and the two-level system. I. Rotation and half-integral spin states,'' {\em Am. J. Phys. \bf 46}, 251 (1978). available on ChaosBook.org/GroupTheory/library/Harper78a.pdf , a year later or so from my own write up. What he does in this pretty paper is to explain how Hamilton (who would have guessed...) used quaternions to to extend the discrete Fourier transform I developed for you in the course for a 1-d circle to the 2-d sphere embedded in 3 dimensions. I do not expect you to work through this, but it is pretty. ---------------------------------------------------------------------- PHYS-7147-13/HarterGrTheo.txt $Author: predrag $ $Date: 2013-11-04 12:32:52 -0500 (Mon, 04 Nov 2013) $