Radial quasipotential equation for a fermion and antifermion and infinitely rising central potentials

Radial equations for a system consisting of a fermion and an antifermion are derived in the quasipotential approach, and the asymptotic behavior of the radial wave functions in the limit $r\to\infty$ for infinitely rising central quasipotentials is investigated. The analogy with the Dirac equation in an external field is studied and it is shown that a confinement type solution is realized only in the presence of a scalar potential. A picture closest to that of the Schrödinger equation is realized if the quasipotential is an equal mixture of a scalar and the fourth component of a vector. The behavior near pole singularities is also investigated.