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

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.

Keywords

Relativistic quantum mechanics; Harmonic oscillator; Special relativity; Analytical solutions

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References

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DOI: https://doi.org/10.20961/jphystheor-appl.v9i2.106236

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