The semi-relativistic equation is cast into a second-order Schrodinger-like
equation with the inclusion of relativistic corrections up to order (v/c)^2.
The resulting equation is solved via the shifted-l expansion technique, which
has been recently developed to get eigenvalues of relativistic and
non-relativistic wave equations. The Coulomb, Oscillator, and the
Coulomb-plus-linear potential used in qq-bar phenomenology are tested. The
method gives quite accurate results over a wide range of r and any choice of
quantum numbers n and l. However, a comparison of the present work with those
of Lucha et al. and Nickisch et al. will serve as a test of this approach.