Geodesic
Floquet asymptotics of solutions of the Schr\"odinger equation in the case of a~semi-infinite crystal
Teoretičeskaâ i matematičeskaâ fizika, Tome 77 (1988) no. 3, pp. 472-478

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For a Schrödinger operator with potential corresponding to a semi-infinite crystal the $x_3\to\pm\infty$ asymptotic behavior of wave functions that have Bloch behavior with respect to $x_1$ and $x_2$ is described. 
@article{TMF_1988_77_3_a13,
     author = {Yu. P. Chuburin},
     title = {Floquet asymptotics of solutions of the {Schr\"odinger} equation in the case of a~semi-infinite crystal},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {472--478},
     publisher = {mathdoc},
     volume = {77},
     number = {3},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_77_3_a13/}
}
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Yu. P. Chuburin. Floquet asymptotics of solutions of the Schr\"odinger equation in the case of a~semi-infinite crystal. Teoretičeskaâ i matematičeskaâ fizika, Tome 77 (1988) no. 3, pp. 472-478. http://geodesic.mathdoc.fr/item/TMF_1988_77_3_a13/