Geodesic
A crystal with a singular potential in a homogeneous electric field
Teoretičeskaâ i matematičeskaâ fizika, Tome 123 (2000) no. 1, pp. 132-149 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the asymptotic behavior of solutions to the one-dimensional Schrödinger equation $-\psi''+q(x)\psi-Fx\psi=E\psi$ for large arguments. We assume that the potential $q$ is a periodic function and is absolutely integrable over the period. We show that the spectral problem for the original Schrödinger equation can be reduced to the spectral problem for a discrete system. If the potential $q$ is smooth, the transition matrix tends to the unit matrix rapidly; if $q$ is not smooth, the transition matrix tends to the unit matrix slowly, and the discrete system demonstrates random properties. This explains why the spectrum of the original equation has remained practically unexplored. 
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A. A. Pozharskii. A crystal with a singular potential in a homogeneous electric field. Teoretičeskaâ i matematičeskaâ fizika, Tome 123 (2000) no. 1, pp. 132-149. http://geodesic.mathdoc.fr/item/TMF_2000_123_1_a11/

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