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TMF, 1999, Volume 120, Number 2, Pages 277–290 (Mi tmf775)  

This article is cited in 6 scientific papers (total in 6 papers)

Schrödinger operator with a perturbed small steplike potential

Yu. P. Chuburin

Physical-Technical Institute of the Ural Branch of the Russian Academy of Sciences

Abstract: We consider the Schrödinger operator with a potential that is periodic with respect to two variables and has the shape of a small step perturbed by a function decreasing with respect to a third variable. We show that under certain conditions on the magnitudes of the step and the perturbation, a unique level that can be an eigenvalue or a resonance exists near the essential spectrum. We find the asymptotic value of this level.

DOI: https://doi.org/10.4213/tmf775

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English version:
Theoretical and Mathematical Physics, 1999, 120:2, 1045–1057

Bibliographic databases:

Received: 27.11.1998

Citation: Yu. P. Chuburin, “Schrödinger operator with a perturbed small steplike potential”, TMF, 120:2 (1999), 277–290; Theoret. and Math. Phys., 120:2 (1999), 1045–1057

Citation in format AMSBIB
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\by Yu.~P.~Chuburin
\paper Schr\"odinger operator with a perturbed small steplike potential
\jour TMF
\yr 1999
\vol 120
\issue 2
\pages 277--290
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\crossref{https://doi.org/10.4213/tmf775}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1737292}
\zmath{https://zbmath.org/?q=an:0991.81022}
\transl
\jour Theoret. and Math. Phys.
\yr 1999
\vol 120
\issue 2
\pages 1045--1057
\crossref{https://doi.org/10.1007/BF02557411}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Arsen'ev, “Resonance Scattering by Infinite Sheets”, Theoret. and Math. Phys., 127:1 (2001), 424–434  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. N. I. Pletnikova, “Ob odnomernom uravnenii Shredingera s nelokalnym potentsialom tipa vozmuschennoi stupenki”, Izv. IMI UdGU, 2004, no. 1(29), 95–108  mathnet
    3. N. I. Pletnikova, “Ob urovnyakh operatora Shredingera na granitse nepreryvnogo spektra”, Izv. IMI UdGU, 2005, no. 1(31), 107–112  mathnet
    4. N. I. Pletnikova, “Zadacha rasseyaniya dlya uravneniya Shredingera s potentsialom tipa vozmuschennoi stupenki”, Izv. IMI UdGU, 2006, no. 1(35), 89–97  mathnet
    5. N. I. Pletnikova, “Issledovanie urovnei operatora Shredingera na granitse nepreryvnogo spektra”, Izv. IMI UdGU, 2006, no. 2(36), 91–94  mathnet
    6. Yu. P. Chuburin, “Electron scattering at the domain wall”, Theoret. and Math. Phys., 166:2 (2011), 234–243  mathnet  crossref  crossref  mathscinet  adsnasa  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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