The Dirac-Moshinsky oscillator: theory and applications

This work summarizes the most important developments in the construction and application of the Dirac-Moshinsky oscillator (DMO). The literature on the subject is voluminous, mostly because of the avenues that exact solvability opens towards our understanding of relativistic quantum mechanics. Here...

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Bibliographic Details
Published inAIP conference proceedings Vol. 1334; no. 1
Main Author Sadurni, Emerson
Format Journal Article
LanguageEnglish
Published United States 21.03.2011
Subjects
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
CRYSTAL LATTICES
CRYSTAL STRUCTURE
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
ELECTRONIC EQUIPMENT
ENERGY RANGE
EQUATIONS
EXACT SOLUTIONS
FIELD EQUATIONS
HEXAGONAL LATTICES
LIE GROUPS
LORENTZ TRANSFORMATIONS
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
MECHANICS
OPTICS
OSCILLATORS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM MECHANICS
QUANTUM OPERATORS
RELATIVISTIC RANGE
SIMULATION
SYMMETRY GROUPS
TRANSFORMATIONS
WAVE EQUATIONS
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Summary:This work summarizes the most important developments in the construction and application of the Dirac-Moshinsky oscillator (DMO). 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. 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.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.3575536