Geodesic
Coordinate asymptotic behavior of the solution of the scattering problem for the Schrödinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 19 (1974) no. 2, pp. 217-232 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {1974},
     volume = {19},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1974_19_2_a7/}
}
TY  - JOUR
AU  - V. S. Buslaev
AU  - M. M. Skriganov
TI  - Coordinate asymptotic behavior of the solution of the scattering problem for the Schrödinger equation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1974
SP  - 217
EP  - 232
VL  - 19
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1974_19_2_a7/
LA  - ru
ID  - TMF_1974_19_2_a7
ER  - 
%0 Journal Article
%A V. S. Buslaev
%A M. M. Skriganov
%T Coordinate asymptotic behavior of the solution of the scattering problem for the Schrödinger equation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1974
%P 217-232
%V 19
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1974_19_2_a7/
%G ru
%F TMF_1974_19_2_a7
V. S. Buslaev; M. M. Skriganov. Coordinate asymptotic behavior of the solution of the scattering problem for the Schrödinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 19 (1974) no. 2, pp. 217-232. http://geodesic.mathdoc.fr/item/TMF_1974_19_2_a7/

[1] V. S. Buslaev, Problemy matematicheskoi fiziki, Sb., Izd-vo LGU, 1966, 82 | MR

[2] A. Ya. Povzner, Matem. sb., 32 (1953), 109 | MR | Zbl

[3] M. M. Skriganov, Tr. Matematicheskogo in-ta im. V. A. Steklova AN SSSR, 125 (1973), 187 | MR | Zbl

[4] V. S. Buslaev, V. B. Matveev, TMF, 2 (1970), 367 | MR

[5] L. D. Landau, E. M. Lifshits, Kvantovaya mekhanika, Fizmatgiz, 1963

[6] F. M. Mors, G. Feshbakh, Metody teoreticheskoi fiziki, t. 2, IL, 1960