On one hole in two dimensional Hubbard model with infinite repulsion

The energy spectrum and wave functions of the two dimensional Hubbard model with infinite repulsion are studied for N x N cluster. The calculations are carried out at pre-assigned total quasi momentum values of α-vector. A set of four non-linear algebraic equations is derived, which describes the energy levels of the cluster. The analyses is reduced to the simplest case αx=αy=α,α=(0,π)