Calculating the Energy Spectrum of Complex Low-Dimensional Heterostructures in the Electric Field

An algorithm for solving the steady-state Schrödinger equation for a complex piecewise-constant potential in the presence of the E-field is developed and implemented. The algorithm is based on the consecutive matching of solutions given by the Airy functions at the band boundaries with the matrix rank increasing by no more than two orders, which enables the characteristic solution to be obtained in the convenient form for search of the roots. The algorithm developed allows valid solutions to be obtained for the electric field magnitudes larger than the ground-state energy level, that is, when the perturbation method is not suitable.