Eigenfunctions parent function

In this case the eigenfunction must hence belong to the complement C(U ) and the parent function F must then be situated in the set A U l) outside the L2 Hilbert space. Substituting the relation = UF into the second relation of Eq. (2.36) and multiplying the left by U one obtains... 

The operator of the perturbed system is written as H = H° + h, where H° is the Hiickel operator of the parent molecule and h the perturbation operator. We could, of course, set up a new Hiickel determinant for the perturbed system, but having the eigenvalues s p and the associated eigenfunctions with the operator H of the parent system at hand, we already have a good starting point for the new system. Therefore, the wavefunctions are set up as linear combinations of the functions i//j° (Equation 4.40). 

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