Periods of relativistic oscillators with even polynomial potentials

The authors modify a non-perturbative variational approach based on the Principle of Minimal Sensitivity to calculate the periods of relativistic oscillators with even polynomial potentials. The optimization of the variational parameter is adapted by introducing additional free parameters whose values are set using the ultrarelativistic limit of the period as a boundary condition. Compact general approximations for the potentials x22+x2m2m, ∑n=1mx2n2n and x2m2m prove to be accurate over the whole solution domain and even for large values of m.