Analytical solutions of relativistic quantum harmonic oscillators - Koffa Durojaiye Jude; O. Ogunjobi; I. Odesanya; E.O Enock; F. Ahmed-Ade; M.M Gwani; I.E Olorunleke (Journal of Physics: Theories and Applications, 2025)
We present analytical solutions for relativistic quantum harmonic oscillators using a Hermite polynomial series approach. Our method yields closed-form energy eigenvalues and normalized eigenfunctions accurate to order , providing improved precision beyond existing first-order relativistic treatments. Through numerical validation, we demonstrate that relativistic corrections become substantial for systems where particle velocities approach appreciable fractions of the speed of light. The theoretical framework offers a foundation for investigating quantum phenomena in relativistic regimes with potential applications to high-energy physics and astrophysics.