English

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}
}

Comments

8 pages, 0 figures

R2 v1 2026-06-21T13:00:54.908Z