Effect of kinetic energy operator on double heterostructures spectra

TL;DR

This paper investigates how the choice of kinetic energy operator affects the energy spectra in double heterostructures with position-dependent mass, using analytical and reflection coefficient methods.

Contribution

It introduces a complementary method for calculating spectra and analyzes the impact of different kinetic energy operators on heterostructure spectra.

Findings

Spectra obtained from the two methods are consistent and complement previous results.

The study includes spectra corresponding to an additional kinetic energy operator.

Methods enable critical analysis of the relevance of various kinetic energy operators.

Abstract

We report on the effect of the kinetic energy operator ambiguity on the energy spectra of various double heterostructures when the mass of the charge carriers, subjected to a potential, depends on position. The spectra are calculated using two complementary techniques. In the first case, which is not always possible, the energy spectrum satisfies a transcendental equation, which is obtained through an analytical process. While in the second, which can be used practically in any double heterostructure (DH), the energy spectra correspond to the poles of the reflection coefficient of the heterostructure. The spectra thus obtained complement those already reported in a previous reference, since we now include the spectra of another kinetic energy operator (KEO). Finally, we show how these methods allow us to critically analyze some statements that have been made about the relevance of some kinetic energy operators in some simpler heterostructures.