Solvable model of the relativistic two-fermion bound-state problem with infinitely rising potentials

A one-time relativistic equation for fermion-antifermion bound states with a special Lorentz structure of the quasipotential is considered. Radial equations free of the Klein paradox are obtained. For states with parity $\varepsilon_P=(-1)^{J+1}$, the equations admit exact analytic solutions. In the case of a linear potential with $J=0$ it is shown for the example of charmonium that the splittings of the excited levels can be smaller than in the nonrelativistic approach.