Abstract
A quantum realization of the relativistic Harmonic oscillator is achieved in terms of the spatial variable x and [Formula: see text] (the minimal canonical representation). The Hamiltonian operator is found (at lower order) by using a perturbative expansion in the constant c-1. Unlike the Foldy–Wouthuysen version of the relativistic hydrogen atom, conventional perturbation theory cannot be applied and a perturbation of the scalar product itself is required to make the theory unitary.
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