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 ${\d\over \d x}$ (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.

9 pages, latex, no figures

References in corpus (1)

• Higher-Order Differential Operators on a Lie Group and Quantization

Cited by in corpus (3)

• Group Approach to the Quantization of the Pöschl-Teller dynamics
• Relativistic Ermakov-Milne-Pinney Systems and First Integrals
• Quantum Field Theory in a Symmetric Curved Space from a Second Quantization on a Group