Solution of a singular quasipotential equation for bound states

The Logunov–Tavkhelidze quasipotential equation for scalar particles of equal masses and a potential $V(r)=gr^{-1}$ in the coordinate representation is reduced to a secondorder differential boundary-value problem in the momentum representation. The corresponding bound-state problem is considered for the $S$-wave. The method of matching solutions is used to obtain a spectrum of weakly bound states; this is similar to the energy spectrum of the Schrödinger equation with the potential $V(r)=-g'r^{-2}$, but differs from it in that the problem of the collapse onto the scattering center does not arise. A comparison equation method is formulated and applied to this problem and used to obtain a discrete energy spectrum for all binding energies.