A method for the calculation of electronic states in a quantum well using the chain model

A method for calculating the electronic states in a quantum well (QW) system is presented based on the tight-binding Hamiltonian within a one-band model and in terms of Dyson's equation. The Hamiltonian for the whole system is separated into two parts: one corresponds to an infinitely pure linear chain and the other describes a finite impurity chain confined to the QW region. The explicit solution to Dyson's equation for the QW can be obtained via a compact recursion relationship. The formulae have been demonstrated using particular examples. From the authors' numerical evaluation of the energy of the quasi-bound states for the QW and comparison with the usual effective-mass approximation, it shows that for both models the results are the same. They believe that their treatment may provide great flexibility for dealing with the problem in heterostructures.