Matrix elements of the secular determinant for trial functions?

[MontavonM]

This is the quantum part for solving wavefunctions of mulit-electron atoms that need to be approximated by the variation method.

Specifically we are supposed to differentiate this equation using the quotient rule :

E(c1,c2) = [(c1^2*H11 + 2c1c2H12 + c2^2*H22) / (c1^2*S11 + 2c1c2*S12 + c2^2S22)]

Our book only shows the way to do it using the product rule after you bring the bottom onto the initial left side of the equation...

H and S are constants, with c as the adjustable variable of the equation... I think.

I've finished the differentiation but I got a different answer than I should have (we were given the answer)... Could anyone refer me to a website or something that shows the quotient rule? Thanks in advance!

 

[azntoon]

The answer using the quotient rule is as follows: E'(c1,c2) = [(2*c1*H11 + 2*c2*H12 - (c1^2*S11 + 2*c1*c2*S12 + c2^2*S22)*(2*c1*H11 + 2*c2*H12)) / (c1^2*S11 + 2*c1*c2*S12 + c2^2*S22)^2]