Geodesic
The scattering problem for a~long-range periodic in time potential
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 11, Tome 84 (1979), pp. 114-116

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The multidimensional Schrödinger operator $H=-\Delta+V(x,t)$ with a time-dependent potential is considered. The potential may decrease slowly with respect to space variable but its mean value in time is equal to zero. It is shown that for the pair $H_0=-\Delta$, $H$ wave operators exist and their ranges coincide with the absolute continuous subspace of the corresponding operator of monodromy. 
@article{ZNSL_1979_84_a9,
     author = {E. L. Korotyaev},
     title = {The scattering problem for a~long-range periodic in time potential},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {114--116},
     publisher = {mathdoc},
     volume = {84},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_84_a9/}
}
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E. L. Korotyaev. The scattering problem for a~long-range periodic in time potential. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 11, Tome 84 (1979), pp. 114-116. http://geodesic.mathdoc.fr/item/ZNSL_1979_84_a9/