Geodesic
Interaction of a free wave with a semicrystall
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 20, Tome 186 (1990), pp. 107-114

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The paper deal with Schroedinger operator with a semiperiodic potential in $L_2(\mathrm{R}^n)$, $n=2$. Incident and reflected waves in a free semispace are constructed. An asymptotic expansion for reflection matrix are given in a high energy region. 
@article{ZNSL_1990_186_a9,
     author = {Yu. E. Karpeshina},
     title = {Interaction of a free wave with a semicrystall},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {107--114},
     publisher = {mathdoc},
     volume = {186},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1990_186_a9/}
}
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Yu. E. Karpeshina. Interaction of a free wave with a semicrystall. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 20, Tome 186 (1990), pp. 107-114. http://geodesic.mathdoc.fr/item/ZNSL_1990_186_a9/