Correlation between perturbation and variation methods in the study of strongly correlated electron systems

The ground–state wave function and energy are calculated for two electrons subject to a one-band Hubbard Hamiltonian on a one dimensional lattice containing N electronic sites, N = 2,3,4,5,6, and a 3 x 3 cluster of the square lattice, using perturbation and variational methods. The results from these two approximation methods are then compared with the result from exact calculational method. Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 583-59