Numerically efficient computation of eigensolution spectrum in one-dimensional heterostructure

We describe a method that allows an efficient determination of the density of states of one-dimensional heterostructures. We show that the propagation of an appropriate vector through the structure together with the use of the node theorem is much more effective than transfer matrix methods in those cases in which highly degenerate spectra are present. As a by-product, spatial behavior of solutions is also easily obtained. A case of elastic propagation is discussed in detail and application to Schrödinger's equation is presented.