Quasi-relativistic harmonic bound states

TL;DR

This paper introduces a new method to analyze quasi-relativistic harmonic oscillator bound states, demonstrating improved results over previous techniques and extending the analysis to states with higher angular momentum.

Contribution

A novel methodological approach for studying quasi-relativistic harmonic bound states, yielding more accurate results than prior methods and including states with larger angular momentum.

Findings

Results are more favorable than previous methods

Bound states with larger angular momenta are constructed

Enhanced accuracy in quasi-relativistic bound state analysis

Abstract

The quasi-relativistic harmonic oscillator bound states constructed by Znojil (J. Phys. A: Math. Gen. 29 (1999)2905) are investigated via a new methodical proposal. Compared with those obtained by an anonymous referee (from a direct numerical integration method)of Znojil's paper, our results appear to be more favourable than those obtained by Znojil via quasi-perturbation, variational, Hill-determinant and Riccati-Pade' methods. Bound states with larger angular momenta l, are also constructed.