Relativistic Ladder Operators for the Three-Dimensional Harmonic Oscillator
Quantum Physics
2009-05-13 v1
Abstract
The quantum constraint equations for a relativistic three-dimensional harmonic oscillator are shown to find concise expression in terms of Lorentz covariant ladder operators. These ladder operators consist of two conjugate 4-vectors that are each constrained to generate three linearly independent combinations of ladder operator components for raising and lowering the eigenstates of the oscillator. Correspondence to the Schr\"{o}dinger equation for the harmonic oscillator in the non-relativistic limit is demonstrated.
Keywords
Cite
@article{arxiv.0905.1750,
title = {Relativistic Ladder Operators for the Three-Dimensional Harmonic Oscillator},
author = {Robert J. Ducharme},
journal= {arXiv preprint arXiv:0905.1750},
year = {2009}
}
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8 pages, 0 figures