The quasi-relativistic harmonic oscillator bound states constructed by Znoj
il (1996 J. Phys. A: Math. Gen. 29 2905) are investigated via a new methodi
cal 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-perturbative,
variational, Hill-determinant and Riccati-Pade methods. Bound states with
larger angular momenta, l, are also constructed.