Emerson Sadurni
Published 2011-01-15Version 1
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.
Comments: Lecture notes from the course "The Dirac-Moshinsky Oscillator: Theory and Applications". To appear in the proceedings of ELAF 2010, Mexico. 28 figures, 45 pages
Journal: AIP Conf.Proc.1334:249-290,2011
Lorentz-covariant deformed algebra with minimal length and application to the 1+1-dimensional Dirac oscillator
Quantum propagator and characteristic equation in the presence of a chain of $δ$-potentials
Huygens-Fresnel-Kirchhoff construction for quantum propagators with application to diffraction in space and time
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