Meson Spectra with the Linear Plus Coulombic Potential in Relativistic Equations.

In this dissertation we solve the Dirac equation for a scalar long-range linear plus a short-range Coulombic potential, by transforming the equation into a Schrodinger -like equation for the small and large components. The equation of the large component is solved numerically by the WKB method. The results are satisfactory for charmonium and upsilon systems, but not for the light mesons. A more desirable equation, the Bethe-Salpeter equation, which is a relativistic equation for two-body systems, is reviewed and solved in the framework of the ladder approximation numerically using the method of Runge-Kutta. The interaction potential which we used is the same as the potential used in the Dirac equation. The mass spectra for various q -q is obtained. We find that it is possible to describe the heavy as well as the light mesons by a unified, flavor -independent potential.