THE SEMIRELATIVISTIC EQUATION VIA THE SHIFTED-l EXPANSION TECHNIQUE

The semirelativistic wave equation which appears in the theory of relativistic quark–antiquark bound states, is cast into a constituent second order Schrödinger-like equation with the inclusion of relativistic corrections up to order (v/c)² in the quarks speeds. The resulting equation is solved via the Shifted-l expansion technique (SLET), which has been recently developed to get eigenvalues and wave functions of relativistic and nonrelativistic wave equations. The Coulomb, Oscillator, and the Coulomb-plus-linear potentials used in 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 analytic expression for the Coulomb ground-state energy problem, a result which is in the right direction at least to serve as a test of this approach.