Coordinate asymptotic behavior of the solution of the scattering problem for the Schrödinger equation

A study is made of the asymptotic behavior of the solution of the scattering problem for a multidimensional Schrödinger equation as $x\to\infty$. The potential is assumed to vary smoothly and decrease more rapidly than the Coulomb potential. The asymptotic behavior of the solution of the scattering problem corresponding to the plane wave eikx contains special functions in the neighborhood of the direction of $k$. The singularities of the scattering amplitude are described; these also arise only in this direction.