SADDLE POINT VARIATIONAL METHOD FOR DIRAC CONFINEMENT

A saddle point variational (SPV) method was applied to the Dirac equation as an example of a fully relativistic equation with both negative and positive energy solutions. The effect of the negative energy states was mitigated by maximizing the energy with respect to a relevant parameter while at the same time minimizing it with respect to another parameter in the wave function. The Cornell potential and a power-law scalar and vector potentials were used in our calculations for the quark confinement. Cares were taken to avoid the Klein paradox by the dominance of the scalar component over the vector part. Two parameters variational method gives excellent and stable results. Our findings for the total energy per unit mass)(mE, relativistic magnetic moment (ra)rr×, electromagnetic energy for a unit charge (1r) and magnetic moment of quarks were in good agreement with the exact solutions.