Geodesic
Solutions of the Schr\"odinger equation in the case of a~semiinfinite crystal
Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 1, pp. 38-47

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It is proved that the bounded solutions of the Bloch type in $x_1$, $x_2$ variables of the Schrödinger equation with the potential which is periodic in the semi-space $\{x_3\geqslant 0\}$ and exponentially decreases when $x_3\to -\infty$, may be approximated by the solutions of the Schrödinger equation which correspond to crystal films with a number of layers tending to infinity. It gives the possibility to find the number of linearly independent solutions of this type under some propositions. 
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     author = {Yu. P. Chuburin},
     title = {Solutions of the {Schr\"odinger} equation in the case of a~semiinfinite crystal},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {38--47},
     publisher = {mathdoc},
     volume = {98},
     number = {1},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_98_1_a3/}
}
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Yu. P. Chuburin. Solutions of the Schr\"odinger equation in the case of a~semiinfinite crystal. Teoretičeskaâ i matematičeskaâ fizika, Tome 98 (1994) no. 1, pp. 38-47. http://geodesic.mathdoc.fr/item/TMF_1994_98_1_a3/