Light and heavy mesons in the context of the quasipotential equation

The numerical solution of the relativistic quasipotential equation is presented. A new approach is introduced to express the Blankenbecler-Sugar-Logunov-Tavkhlidze equation and the equal-time equation which is equivalent to the full Salpeter equation, improved by adding the crossed box diagram as energy eigenstates. A set of coupled positive and negative energy eigenstates is obtained. A systematic method to solve the nonlinear eigenvalue problem of the bound state equation is given and the results are compared with the approximate versions of the standard eigenvalue of the bound state. These equations are used in the investigation of heavy and light mesons with vector Coulomb and scalar linear confining potentials. © 1996 The American Physical Society.