The quasi-static connection of two important systems

Tb begin let us write two Hamiltonians that are certainty very important for our goal the first is the total Hamiltonian of our qfstem (of course, with the Coulombic electron-electron interactions). Let us denote the operator for some reasons as H(X = 1), cf. eqs. (11.6) and (11.7)  

The second Hamiltonian H( = 0) pertains to the Kohn-Sham fictitious qfstem of the non-interaaing electrons (it contains our wonder vq, which we solemnty promise to search for, and the kinetic energy operator and. ..nothing else, cf. eq. (11.14))  

We will try to connect these two important systems by generating some intermediate Hamiltonians H(A) for A intermediate between 0, and 1  

that our electrons are not real for intermediate values of A (each electron carries the electric charge VA). 

The intermediate Hamiltonian H(X) contains a mysterious v, which generates the exact density distribution p that corresponds to the Hamiltonian H X = 1), i.e. with all interactions in place. The same exact p corresponds to//(A = 0). 

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