Geodesic
Scattering problem for radial Schrödinger equation with a slowly decreasing potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 10 (1972) no. 2, pp. 238-248 Cet article a éte moissonné depuis la source Math-Net.Ru

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The scattering problem for the Schrodinger equation with slowly decreasing potential is considered. Stationary wave operators $W_{\pm}(H,H_0)$ are constructed and their completeness is proved. It is shown that the operators $W_{\pm}(H,H_0)$ can also be defined as the limits $W_{\pm}(H,H_0)=\lim{t\to\pm\infty} \exp(itH)T_{\pm}\exp(-itH_0)$, $T_{\pm}$ being some operators, which do not depend on $t$, do not commute with $H_0$ and can be constructed explicity for the :given potential $q(x)$.The invariance principle for the wave operators $W_{\pm}$ is proved. 
@article{TMF_1972_10_2_a8,
     author = {V. B. Matveev and M. M. Skriganov},
     title = {Scattering problem for radial {Schr\"odinger} equation with a slowly decreasing potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {238--248},
     year = {1972},
     volume = {10},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1972_10_2_a8/}
}
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V. B. Matveev; M. M. Skriganov. Scattering problem for radial Schrödinger equation with a slowly decreasing potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 10 (1972) no. 2, pp. 238-248. http://geodesic.mathdoc.fr/item/TMF_1972_10_2_a8/

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