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A Perturbative Approach to the Relativistic Harmonic Oscillator

J. Guerrero·V. Aldaya
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Abstract

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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J. Guerrero, V. Aldaya. 1998-02-04. A Perturbative Approach to the Relativistic Harmonic Oscillator. https://doi.org/10.1142/s0217732399001784

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