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All Journal Journal of Physics: Theories and Applications
M.M Gwani
Federal University Lokoja, Kogi State, Nigeria
Education Materials Science & Nanotechnology Physics

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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 Vol 9, No 2 (2025): Journal of Physics: Theories and Applications
Publisher : Universitas Sebelas Maret

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20961/jphystheor-appl.v9i2.106236

Abstract

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.
Co-Authors E.O Enock F. Ahmed-Ade I. Odesanya I.E Olorunleke Koffa Durojaiye Jude O. Ogunjobi