The Set of Three Coulson Orthogonal Hybrids

Comparison with our set (Equations 2.219) shows that, if the two sets have to be equivalent, we must have  

We notice, first, that hybrids (Equations 2.299) are correctly normalized, and that  

Schmidt orthogonalization of / to b or b2 can be done using the explicit formulae given elsewhere (Magnasco, 2007), so obtaining  

It can be seen that, in doing the orthogonalization process, the coefficient of y in (Equatrions 2.304) becomes identically zero, and we obtain 

1= (1—2S ) [s(cosft —2Ssinft )—2 (sinft + 25cosft cos0)] (2.305) Using Equations (2.300) and (2.214) it is further easily verified that  

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