Geodesic
Limits of applicability of the tight binding approximation for complex-valued potential function
Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 3, pp. 448-466

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We consider a one-dimensional Schrödinger operator with periodic potential that is constructed as a sum of shifts of a given complex-valued potential $q\in L^1(\mathbf R)$. A mathematical basis of the tight binding approximation in this case is given. Let $\lambda_0$ be an isolated eigenvalue of Schrödinger operator with potential $q$. Then for the operator with periodic potential there exists a continuos spectrum that lies near $\lambda_0$. An asymptotic behavior of this part of the spectrum for the cases of one- and two-dimensional invariant subspace corresponding to $\lambda_0$ when the period tends to infinity is studied. 
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     author = {A. L. Mironov and V. L. Oleinik},
     title = {Limits of applicability of the tight binding approximation for complex-valued potential function},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {448--466},
     publisher = {mathdoc},
     volume = {112},
     number = {3},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1997_112_3_a7/}
}
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A. L. Mironov; V. L. Oleinik. Limits of applicability of the tight binding approximation for complex-valued potential function. Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 3, pp. 448-466. http://geodesic.mathdoc.fr/item/TMF_1997_112_3_a7/