Geodesic
Semicrystal with a~singular potential in an accelerating electric field
Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 3, pp. 410-428

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We study the Schrödinger equation describing the one-dimensional motion of a quantum electron in a periodic crystal placed in an accelerating electric field. We describe the asymptotic behavior of equation solutions at large values of the argument. Analyzing the obtained asymptotic expressions, we present rather loose conditions on the potential under which the spectrum of the corresponding operator is purely absolutely continuous and spans the entire real axis.
Keywords: Schrödinger equation, asymptotic solution, turning point, absolutely continuous spectrum.
Mots-clés : adiabatic solution 
@article{TMF_2006_146_3_a4,
     author = {A. A. Pozharskii},
     title = {Semicrystal with a~singular potential in an accelerating electric field},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {410--428},
     publisher = {mathdoc},
     volume = {146},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2006_146_3_a4/}
}
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A. A. Pozharskii. Semicrystal with a~singular potential in an accelerating electric field. Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 3, pp. 410-428. http://geodesic.mathdoc.fr/item/TMF_2006_146_3_a4/