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.
Categories: math-ph hep-th math.MP