The number of energy levels of a particle in a uniform MQW structure

Abstract

A recently obtained multilayer equation that gives the eigenvalues of the energy of a quantum particle in an arbitrary one-dimensional piecewise constant potential field is studied. In particular, this equation can be used to calculate the eigenvalues of the particle’s energy in an MQW structure, in which the potential takes only two different values in the various layers. A formula is analyzed that was obtained earlier by the author for the number of energy levels in a uniform MQW structure, i.e., in a structure with potential wells and walls of constant widths. The equation is substantiated for all uniform MQW structures. It is proved that the number of energy levels in a uniform MQW structure increases indefinitely with unlimited growth of the number of potential wells. The existence of uniform MQW structures with an arbitrarily large prescribed number of potential wells and with a single energy level is proved.