On the density of states of the heterojunction of two amorphous solids

An efficient algorithm to solve Schrödinger´s equation in one dimension, for arbitrary shape potential, by making it stepwise constant, is presented. The algorithm is applied to sets of rectangular potential wells that have pseudorandom changes either in the distance between them or in their height. In both cases, for the finite sets of wells considered, localization is generally the rule, though exceptions were found. The heterojunction resulting from putting together two of these well sets, one of each type of randomness, may have a global density of states that is not the sum of those of the constituent well sets, since a zone where the density decreases forms near the bottom of the band