Calculation of the Energy Spectrum of Quantum Particle in Double Potential Pit

Abstract

The problem of quantum particle in infinitely deep potential pit with an internal potential barrier of finite height is solved. The solution is performed in a simple algorithmic approach, which allows you to use the result in the study of semiconductor nanostructures. The real heterostructure corresponding to this model should look like thin layer of wideband semiconductor placed between two slightly thicker layers of narrowband semiconductor. To ensure the 'infinite depth' of the potential pit, layers of conductor must be applied to the outer side surfaces of the triple semiconductor heterostructure and negative electric potential must be applied. Another option for the practical implementation of the model can be done by placing two electrons in one potential pit. In this case, the pit is a local space, at the boundary of which negative electric potential is applied. The internal potential barrier arises due to the Coulomb interaction of electrons. An example of such a structure is a nanopore on the surface, or in the volume of a metal sample.