Geodesic
Wave operators for the Schr\"odinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 45 (1980) no. 2, pp. 224-234

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A new definition of wave operators directly connected with the asymptotics of solutions of non-stationary Schrödinger equation at large times is suggested. The existence of such wave operators is proved for time-dependent long-range (in particular, multi-particle) potentials. Connection with the traditional wave operators is established. Local wave operators corresponding to an arbitrary open set in configuration space are also considered. 
@article{TMF_1980_45_2_a6,
     author = {D. R. Yafaev},
     title = {Wave operators for the {Schr\"odinger} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {224--234},
     publisher = {mathdoc},
     volume = {45},
     number = {2},
     year = {1980},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1980_45_2_a6/}
}
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D. R. Yafaev. Wave operators for the Schr\"odinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 45 (1980) no. 2, pp. 224-234. http://geodesic.mathdoc.fr/item/TMF_1980_45_2_a6/