  A simple model is presented to investigate an impact of the double occupied
sites on the ground state energy of a lattice. The model is seen as a useful
tool to introduce undergraduate or graduate physics students to an array of a
relatively simple mathematical apparatus and physical ideas which they can
choose later for a deeper study. Instead of analyzing a system of electrons in
a periodic potential, a system of sites having different energy states related
to a number of extra electrons at a site is considered. The simplification is
achieved by introducing operators for one-electron sites and two-electron sites
as independent entities. A simple modeling function for the ground state of the
system is constructed. Linear and quadratic lattices are considered. For a
quadratic lattice the existence of a critical temperature is shown.
