  The scattering problem for two particles interacting via the Coulomb
potential is examined for the case where the potential has a sharp cut-off at
some distance. The problem is solved for two complimentary situations, firstly
when the interior part of the Coulomb potential is left in the Hamiltonian and,
secondly, when the long range tail is considered as the potential. The partial
wave results are summed up to obtain the wave function in three dimensions. It
is shown that in the domains where the wave function is expected to be
proportional to the known solutions, the proportionality is given by an
operator acting on the angular part of the wave function. The explicit
representation for this operator is obtained in the basis of Legendre
polynomials. We proposed a driven Schr\"odinger equation including an
inhomogeneous term of the finite range with purely outgoing asymptotics for its
solution in the case of the three dimensional scattering problem with long
range potentials.
