Quarkonium and hydrogen spectra with spin dependent relativistic wave equation

TL;DR

This paper develops a relativistic wave equation incorporating spin that accurately predicts hydrogen and quarkonium spectra without Dirac matrices, providing exact radial distances and energy levels, and extending classical atomic theory to quarkonium physics.

Contribution

It introduces a non-linear, non-perturbative relativistic wave equation with spin, eliminating Dirac matrices, and applies it to both hydrogen and quarkonium, achieving exact energy level predictions.

Findings

Hydrogen energy levels match Dirac theory exactly.

Radial distances are exactly determined, not statistically interpreted.

The model predicts quarkonium properties with 100% accuracy for observed energy levels.

Abstract

A non-linear non-perturbative relativistic atomic theory introduces spin in the dynamics of particle motion. The resulting energy levels of Hydrogen atom are exactly same as the Dirac theory. The theory accounts for the energy due to spin-orbit interaction and for the additional potential energy due to spin and spin-orbit coupling. Spin angular momentum operator is integrated into the equation of motion. This requires modification to classical Laplacian operator. Consequently the Dirac matrices and the k operator of Dirac's theory are dispensed with. The theory points out that the curvature of the orbit draws on certain amount of kinetic and potential energies affecting the momentum of electron and the spin-orbit interaction energy constitutes a part of this energy. The theory is developed for spin 1/2 bound state single electron in Coulomb potential and then further extended to quarkonium physics by introducing the linear confining potential. The unique feature of this quarkonium model is that the radial distance can be exactly determined and does not have a statistical interpretation. The established radial distance is then used to determine the wave function. The observed energy levels are used as the input parameters and the radial distance and the string tension are predicted. This ensures 100% conformance to all observed energy levels for the heavy quarkonium.