A convolution technique for the calculation of local densities of states

A convolution technique is proposed for the calculation of local densities of states (LDOS) within the tight-binding (TB) model. It relies on the sepa rability of the variables in the Hamiltonian. This technique allows one to carry out calculations for the two- and three-dimensional lattices if the o ne-dimensional LDOS is known. The approach avoids K-space integration as we ll as the processing of large clusters. The results are checked against kno wn results produced by the straight TB model, and some new cases, such as t hat of the LDOS for a two-dimensional lattice in the presence of an externa l electric field, are also considered.