A Perturbative Approach to the Relativistic Harmonic Oscillator
Abstract
A quantum realization of the Relativistic Harmonic Oscillator is realized in terms of the spatial variable x and 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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