Analytical solutions of relativistic quantum harmonic oscillators

Koffa Durojaiye Jude (Federal University Lokoja, Kogi State, Nigeria)
O. Ogunjobi (Federal University Lokoja, Kogi State, Nigeria, Department of Physics and Astronomy, University of Calgary, Canada)
I. Odesanya (Federal University Lokoja, Kogi State, Nigeria)
E.O Enock (Federal University Lokoja, Kogi State, Nigeria Osun State University, Osogbo, Nigeria)
F. Ahmed-Ade (Federal University Lokoja, Kogi State, Nigeria)
M.M Gwani (Federal University Lokoja, Kogi State, Nigeria)
I.E Olorunleke (Federal University Lokoja, Kogi State, Nigeria)

Journal of Physics: Theories and Applications
Vol 9, No 2 (2025): Journal of Physics: Theories and Applications

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.