The Dirac-Moshinsky Oscillator: Theory and Applications

TL;DR

This paper reviews the development, extensions, and applications of the Dirac-Moshinsky oscillator, highlighting its significance in relativistic quantum mechanics and its use in modeling systems like graphene and quantum optics.

Contribution

It provides a comprehensive chronological overview of the Dirac-Moshinsky oscillator, including new exactly solvable extensions and applications in modern physical systems.

Findings

Exact solvability aids understanding of relativistic quantum systems

Extensions to many-particle models are developed

Applications include emulation of graphene in electromagnetic billiards

Abstract

This work summarizes the most important developments in the construction and application of the Dirac-Moshinsky oscillator (DMO) with which the author has come in contact. The literature on the subject is voluminous, mostly because of the avenues that exact solvability opens towards our understanding of relativistic quantum mechanics. Here we make an effort to present the subject in chronological order and also in increasing degree of complexity of its parts. We start our discussion with the seminal paper by Moshinsky and Szczepaniak and the immediate implications stemming from it. Then we analyze the extensions of this model to many particles. The one-particle DMO is revisited in the light of the Jaynes-Cummings model in quantum optics and exactly solvable extensions are presented. Applications and implementations in hexagonal lattices are given, with a particular emphasis in the emulation of graphene in electromagnetic billiards.