What is the Linear Variation Method in Molecular Quantum Mechanics?

[Morten]

In the chapter 9-5 "The Linear Variation Method" p. 363 from the book: Basic Principles and Techniques of Molecular Quantum Mechanics by Ralph Christoffersen, the first thing he does is to minimize the energy, E = c^†Hc/c^†Sc, by requiring its derivative with respect to the coefficient c_p^* to equal zero. He claims the following expression:
dE/dc_p^* (c^†Sc) + E d/dc_p^* (c^†Sc) = d/dc_p^* (c^†Hc) , whereas, by the quotient rule, I would claim:
((dE/dc_p^*)(c^†Hc)(c^†Sc) - (c^†Hc) dE/dc_p^*(c^†Sc)) / (c^†Sc)² = 0 , am I perhaps wrong?

 

[Morten]

The thing was, Ralph indicated strongly the action of setting the derivate equal to zero in that expression but this was postponed to later on in the book as I just read, that was what confused me. For this I am sorry