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Asymptotics of the bound state induced by <i></i>-interaction supported on a weakly deformed plane

Pavel Exner Sylwia Kondej Vladimir Lotoreichik

Analysis of PDEs mathscidoc:1910.43214

Journal of Mathematical Physics, 59, (1), 013501, 2018.1
In this paper, we consider the three-dimensional Schrdinger operator with a -interaction of strength &gt; 0 supported on an unbounded surface parametrized by the mapping R2x(x,f(x)), where 0, and f:R2R, f 0, is a C2-smooth, compactly supported function. The surface supporting the interaction can be viewed as a local deformation of the plane. It is known that the essential spectrum of this Schrdinger operator coincides with 142,+. We prove that for all sufficiently small &gt; 0, its discrete spectrum is non-empty and consists of a unique simple eigenvalue. Moreover, we obtain an asymptotic expansion of this eigenvalue in the limit 0+. In particular, this eigenvalue tends to 142 exponentially fast as 0+.
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@inproceedings{pavel2018asymptotics,
  title={Asymptotics of the bound state induced by <i></i>-interaction supported on a weakly deformed plane},
  author={Pavel Exner, Sylwia Kondej, and Vladimir Lotoreichik},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020133541826500743},
  booktitle={Journal of Mathematical Physics},
  volume={59},
  number={1},
  pages={013501},
  year={2018},
}
Pavel Exner, Sylwia Kondej, and Vladimir Lotoreichik. Asymptotics of the bound state induced by <i></i>-interaction supported on a weakly deformed plane. 2018. Vol. 59. In Journal of Mathematical Physics. pp.013501. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020133541826500743.
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