Geodesic
Electron scattering by a~crystal layer
Teoretičeskaâ i matematičeskaâ fizika, Tome 176 (2013) no. 3, pp. 444-457

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We consider the one-particle discrete Schrödinger operator $H$ with a periodic potential perturbed by a function $\varepsilon W$ that is periodic in two variables and exponentially decreasing in the third variable. Here, $\varepsilon$ is a small parameter. We study the scattering problem for $H$ near the point of extremum with respect to the third quasimomentum coordinate for a certain eigenvalue of the Schrödinger operator with a periodic potential in the cell, in other words, for the small perpendicular component of the angle of particle incidence on the potential barrier $\varepsilon W$. We obtain simple formulas for the transmission and reflection probabilities.
Keywords: discrete Schrödinger operator, perturbed periodic operator, transmission probability, reflection probability. 
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     author = {T. S. Tinyukova and Yu. P. Chuburin},
     title = {Electron scattering by a~crystal layer},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {444--457},
     publisher = {mathdoc},
     volume = {176},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2013_176_3_a8/}
}
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T. S. Tinyukova; Yu. P. Chuburin. Electron scattering by a~crystal layer. Teoretičeskaâ i matematičeskaâ fizika, Tome 176 (2013) no. 3, pp. 444-457. http://geodesic.mathdoc.fr/item/TMF_2013_176_3_a8/