Abstract
We investigate the energies and wavefunctions of a structure consisting of one small cubic box centered on top of another larger with a uniform potential inside. This model is a representation of a quantum pillar on a substrate, a nanostructure with potential device applications. We find that the eigenstates are localized in one or the other of the boxes. Those in the large box are very well localized while those in the small are moderately so. Their energy and localization are studied with respect to the ratio of sides of the two boxes and compared with the results obtained with the small box closed by all sides.