Geodesic
The spectrum of the Schrödinger operator with a rapidly oscillating compactly supported potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 1, pp. 58-63 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the effect of an eigenvalue appearing from the boundary of the essential spectrum of the Schrödinger operator perturbed by a rapidly oscillating compactly supported potential. We prove sufficient conditions for the existence and absence of such an eigenvalue and obtain the first few terms of its asymptotic expansion for the case where this eigenvalue exists.
Keywords: Schrödinger operator, spectrum, asymptotic behavior.
Mots-clés : perturbation 
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     title = {The spectrum of the {Schr\"odinger} operator with a~rapidly oscillating compactly supported potential},
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D. I. Borisov; R. R. Gadyl'shin. The spectrum of the Schrödinger operator with a rapidly oscillating compactly supported potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 1, pp. 58-63. http://geodesic.mathdoc.fr/item/TMF_2006_147_1_a3/

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