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Teoreticheskaya i Matematicheskaya Fizika, 2006, Volume 147, Number 1, Pages 58–63
DOI: https://doi.org/10.4213/tmf2022 (Mi tmf2022) 		 
This article is cited in 17 scientific papers (total in 17 papers)

The spectrum of the Schrödinger operator with a rapidly oscillating compactly supported potential

D. I. Borisov, R. R. Gadyl'shin

Bashkir State Pedagogical University
Full-text PDF (135 kB) Citations (17)
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DOI: https://doi.org/10.4213/tmf2022
Abstract: 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, perturbation, asymptotic behavior.
Received: 22.07.2005
English version:
Theoretical and Mathematical Physics, 2006, Volume 147, Issue 1, Pages 496–500
DOI: https://doi.org/10.1007/s11232-006-0056-y
Bibliographic databases:
Language: Russian
Citation: D. I. Borisov, R. R. Gadyl'shin, “The spectrum of the Schrödinger operator with a rapidly oscillating compactly supported potential”, TMF, 147:1 (2006), 58–63; Theoret. and Math. Phys., 147:1 (2006), 496–500
Citation in format AMSBIB
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    • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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