  We present a numerical scheme for the Hubbard model that throws light on the
rather esoteric nature of the Upper and Lower Hubbard bands that have been
invoked often in literature. We present a self consistent solution of the
ladder diagram equations for the Hubbard model, and show that these provide, at
least in the limit of low densities of particles, a vivid picture of the
Hubbard split bands. We also address the currently topical problem of decay of
the doublon states that are measured in optical trap studies, using the ladder
scheme and also by an exact two particle calculation of a relevant Greens
function.
