A. L. Mironov, V. L. Oleinik, “Limits of applicability of the tight binding approximation for complex-valued potential function”, TMF, 1997, Volume 112, Number 3,Pages <nobr>448

This article is cited in 2 papers

Limits of applicability of the tight binding approximation for complex-valued potential function

A. L. Mironov^a, V. L. Oleinik^b

^a Saint-Petersburg State University
^b St. Petersburg State University, Faculty of Physics

Abstract: 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.

Received: 26.02.1997

DOI: 10.4213/tmf1055