A Perturbative Approach to the Relativistic Harmonic Oscillator

Details A Perturbative Approach to the Relativistic Harmonic Oscillator A Perturbative Approach to the Relativistic Harmonic Oscillator

1998-02-04

arxiv.org/abs/physics/9802010v1

Mod.Phys.Lett. A14 (1999) 1689-1699

Physics

Mathematical Physics

9 pages, latex, no figures

Scientific paper

10.1142/S0217732399001784

A quantum realization of the Relativistic Harmonic Oscillator is realized in terms of the spatial variable $x$ and ${\d\over \d x}$ (the minimal canonical representation). The eigenstates of the Hamiltonian operator are found (at lower order) by using a perturbation expansion in the constant $c^{-1}$. Unlike the Foldy-Wouthuysen transformed version of the relativistic hydrogen atom, conventional perturbation theory cannot be applied and a perturbation of the scalar product itself is required.

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