Strong-coupling asymptotic expansion for schrdinger operators with a singular interaction supported by a curve in 3

Pavel Exner S Kondej

TBD mathscidoc:1910.43101

Reviews in Mathematical Physics, 16, (5), 559-582, 2004.6
We investigate a class of generalized Schrdinger operators in L<sup>2</sup>(<sup>3</sup>) with a singular interaction supported by a smooth curve . We find a strong-coupling asymptotic expansion of the discrete spectrum in the case when is a loop or an infinite bent curve which is asymptotically straight. It is given in terms of an auxiliary one-dimensional Schrdinger operator with a potential determined by the curvature of . In the same way, we obtain asymptotics of spectral bands for a periodic curve. In particular, the spectrum is shown to have open gaps in this case if is not a straight line and the singular interaction is strong enough.
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@inproceedings{pavel2004strong-coupling,
  title={STRONG-COUPLING ASYMPTOTIC EXPANSION FOR SCHRDINGER OPERATORS WITH A SINGULAR INTERACTION SUPPORTED BY A CURVE IN 3},
  author={Pavel Exner, and S Kondej},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020125920135951630},
  booktitle={Reviews in Mathematical Physics},
  volume={16},
  number={5},
  pages={559-582},
  year={2004},
}
Pavel Exner, and S Kondej. STRONG-COUPLING ASYMPTOTIC EXPANSION FOR SCHRDINGER OPERATORS WITH A SINGULAR INTERACTION SUPPORTED BY A CURVE IN 3. 2004. Vol. 16. In Reviews in Mathematical Physics. pp.559-582. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020125920135951630.
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