The semirelativistic equation via the shifted-l expansion technique

The semirelativistic wave equation which appears in the theory of relativis tic quark-antiquark bound states, is cast into a constituent second order S chrodinger-like equation with the inclusion of relativistic corrections up to order (v/c)(2) in the quarks speeds. The resulting equation is solved vi a the Shifted-l expansion technique (SLET), which has been recently develop ed to get eigenvalues and wave functions of relativistic and nonrelativisti c wave equations. The Coulomb, Oscillator, and the Coulomb-plus-linear pote ntials used in q (q) over bar phenomenology are tested. It is observed that , the energy eigenvalues can be explained well upon the more commonly used nonrelativistic models, when such a dynamical relativistic corrections are introduced. In particular, it provides a remarkable accurate and simple ana lytic expression for the Coulomb ground-state energy problem, a result whic h is in the right direction at least to serve as a test of this approach.