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A very nice discussion of everything in the thread above is given by Sakurai in his 1993 edition of Mod. Qu. Mech. For the complex conjugation operator, see the text starting with Eq. (4.4.14) through (4.4.20). And then for time reversal, see Eqs. (4.4.62) - (4.4.65). The background on spin 1/2...