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The shape and size dependence of optical properties in the PbSe material system.In this paper we present a theoretical study aimed of the effects of shape and size on the electronic properties of PbSe. We calculate the eigenvalues and eigenvectors of PbSe spheres and cubes over a range of size in the nanometer range. We analyze the eigenvalues and eigenvectors to determine the densities of electronics states and electron distribution in the various nanostructures. For many years it has been possible to calculate the energy levels in very large crystal structures. Calculations are formed on a single "cell" of the structure that is repeated infinitely in each direction using periodic boundary conditions. This was good enough because the crystals were large and contained and enormous numbers of cells. Two things have happened: experimentalists have been able to grow smaller crystals which contain a much smaller number of cells; and computers have become fast enough to calculate all of the energy levels inside a small crystal. In this work we use the Tight Binding method to study PbSe nanostructures containing hundreds to 1000 atoms. The Tight Binding method (described in section 2.2) allows us to represent the interactions between the atoms in a simple matrix form. The eigenvalues and eigenvectors of the matrix (which we calculate using the Matlab package) then tell us many of the theoretical electronics properties of the materials.. 
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