Spherically Symmetric Approximation (and beyond) in Relativistic Schroedinger Theory

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.