Quantization of the relativistic harmonic oscillator by perturbative methods with application to van der Waals forces

Abstract

The relativistic effects on the quantization of the harmonic oscillator are determined from a perturbation calculation using matrices obtained in the nonrelativistic case. One finds that the energy levels are no longer evenly spaced although the usual transition rules still hold. When a system of two oscillators is considered and the relativistic modification together with radiation effects to second order on the energy of the system is determined, it is found that the higher order correction terms to van der Waals forces are both repulsive and show a dependence on separation distance of 1 R 5 and 1 R 7 .