Periods of relativistic oscillators with even polynomial potentials

TL;DR

This paper introduces a modified non-perturbative method to accurately calculate the periods of relativistic oscillators with even polynomial potentials, using the ultrarelativistic limit for optimization.

Contribution

It develops an improved variational approach based on the Principle of Minimal Sensitivity, applicable to a broad class of relativistic oscillators with polynomial potentials.

Findings

Accurate period approximations across the entire potential class

Effective use of ultrarelativistic limit as a boundary condition

Enhanced non-perturbative calculation method

Abstract

We modify a non-perturbative approach based on the Principle of Minimal Sensitivity to calculate the periods of relativistic oscillators with even polynomial potentials of general form. The optimization of the variational parameter is adapted by using the ultrarelativistic limit of the period as a boundary condition, which determines the values of additional free parameters introduced. Resulting general approximations prove to be accurate over the whole solution domain and for the whole class of potentials.