On the validity of the reduced Salpeter equation

We adapt a general method to solve both the full and reduced Salpeter equations and systematically explore the conditions under which these two equations give equivalent results in meson dynamics. The effects of constituent mass, angular momentum state, type of interaction, and the nature of confinement are all considered in an effort to clearly delineate the range of validity of the reduced Salpeter approximations. We find that for $J\not{\hspace*{-1.0mm}=}0$ the solutions are strikingly similar for all constituent masses. For zero angular momentum states the full and reduced Salpeter equations give different results for small quark mass especially with a large additive constant coordinate space potential. We also show that $\frac{1}{m}$ corrections to heavy-light energy levels can be accurately computed with the reduced equation.Comment: Latex (uses epsf macro), 24 pages of text, 12 postscript figures included. Slightly revised version, to appear in Phys. Rev.

On the instantaneous Bethe-Salpeter equation

We present a systematic algebraic and numerical investigation of the instantaneous Bethe-Salpeter equation. Emphasis is placed on confining interaction kernels of the Lorentz scalar, time component vector, and full vector types. We explore stability of the solutions and Regge behavior for each of these interactions, and conclude that only time component vector confinement leads to normal Regge structure and stable solutions.Comment: Latex (uses epsf macro), 26 pages of text, 12 postscript figures included