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Spectral estimates for a class of Schrdinger operators with infinite phase space and potential unbounded from below

Pavel Exner Diana Barseghyan

TBD mathscidoc:1910.43161

Journal of Physics A: Mathematical and Theoretical, 45, (7), 075204, 2012.2
We analyse two-dimensional Schrdinger operators with the potential| xy| p (x 2+ y 2) p/(p+ 2) where p 1 and 0. We show that there is a critical value of such that the spectrum for < crit is bounded below and purely discrete, while for > crit it is unbounded from below. In the subcritical case, we prove upper and lower bounds for the eigenvalue sums.
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@inproceedings{pavel2012spectral,
  title={Spectral estimates for a class of Schrdinger operators with infinite phase space and potential unbounded from below},
  author={Pavel Exner, and Diana Barseghyan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020131858797999690},
  booktitle={Journal of Physics A: Mathematical and Theoretical},
  volume={45},
  number={7},
  pages={075204},
  year={2012},
}
Pavel Exner, and Diana Barseghyan. Spectral estimates for a class of Schrdinger operators with infinite phase space and potential unbounded from below. 2012. Vol. 45. In Journal of Physics A: Mathematical and Theoretical. pp.075204. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020131858797999690.
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