Geodesic
Coordinate asymptotic behavior of the solution of the scattering problem for the Schr\"odinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 19 (1974) no. 2, pp. 217-232

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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. 
@article{TMF_1974_19_2_a7,
     author = {V. S. Buslaev and M. M. Skriganov},
     title = {Coordinate asymptotic behavior of the solution of the scattering problem for the {Schr\"odinger} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {217--232},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1974_19_2_a7/}
}
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V. S. Buslaev; M. M. Skriganov. Coordinate asymptotic behavior of the solution of the scattering problem for the Schr\"odinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 19 (1974) no. 2, pp. 217-232. http://geodesic.mathdoc.fr/item/TMF_1974_19_2_a7/