Article
Ufa Mathematical Journal
Volume 7, Number 4, pp. 24-31
On perturbation of Schr\"odinger operator on axis by narrow potentials
Bikmetov A.R., Khusnullini I.Kh., Vil'danova V.F.
DOI:10.13108/2015-7-4-24
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We consider a Schr\"odinger operator
on the axis with two complex-valued potentials depending on two small parameters. One of these parameters describes the length of the supports of the potentials, while the other corresponds to the maximal values of the absolute values of the potentials. We obtain the sufficient condition ensuring the emergence of an eigenvalues from the threshold of the essential spectrum. The asymptotics for this eigenvalue is constructed.