Spherically Symmetric Approximation (and beyond) in Relativistic Schroedinger Theory

TL;DR

This paper examines the energy levels of positronium using Relativistic Schroedinger Theory, finding small deviations from conventional quantum predictions that are expected to decrease with more refined approximations.

Contribution

It applies RST to positronium energy calculations and compares results with standard quantum theory, highlighting small deviations and potential for further accuracy.

Findings

RST predicts positronium energies within 3% of quantum theory for n=2 to 30

Deviations are expected to decrease with higher-order approximations

Results suggest RST can closely approximate conventional quantum results

Abstract

The energy eigenvalue problem of non-relativistic positronium is considered within the framework of Relativistic Schroedinger Theory (RST), and the results are compared to those of the conventional quantum theory. For the range of princi- pal quantum numbers n = 2;3;::: ;30, the RST predictions for the non-relativistic positronium energies deviate now from the corresponding predictions of the conven- tional quantum theory at an average of (roughly) 3%. These results suggest that the deviations will be further diminished in the higher orders of approximation.