Linearization of the Relativistic Oscillator Hierarchy

TL;DR

This paper extends MacColl's relativistic harmonic oscillator solution to more complex attractive oscillators, including quartic ones, using a simple linearization map, broadening the applicability of relativistic oscillator models.

Contribution

It introduces a straightforward extension of the linearization method to all attractive oscillators in the relativistic framework, expanding prior solutions beyond harmonic cases.

Findings

Extended MacColl's solution to quartic oscillators.

Unified approach for all attractive oscillators in relativistic context.

Simplified linearization map applicable to various oscillator potentials.

Abstract

This paper is based on MacColl's [1] solution of the equation of motion for a linear (harmonic) oscillator subject to the laws of special relativity in the rest frame of the center of attraction. MacColl's result can be extended to the quartic oscillator in this frame with one extremely simple adjustment of the linearization map given in Anderson [2]. In fact, it can be extended to all the attractive oscillators in this frame.