Approximate States of the Hubbard Model from Heisenberg's Equation

Operators which add electrons with definite energies to states of interacting electrons are solutions of the time-independent Heisenberg equation. Expanding the operators in the number of electron-hole pairs generated to screen each added electron provides systematic approximations for the energies of these operators. This is illustrated for the simplest Hubbard model on a cubic lattice by relations between the energies and electron densities of ground states.