Approximate analytical solution of the one-dimensional quasipotential equation with the potential $(\rho^2+\rho_0^2)^{-1}$ in the relativistic configurational representation

The approximate analytical solutions of the one-dimensional Logunov-Tavkhelidze equation in integral form, that describes bound states, with a model potential of the form$(\rho^2+\rho_0^2)^{-1}$ in the relativistic configuration representation are found. To solve the problem an approximate transformation of the relativistic integral equation in the momentum representation to the Sturm–Liouville problem for the Schrödinger equation with a potential in the form of the modified Pöschl–Teller potential well is performed.