Spectral estimates for a class of Schr\"odinger operators with infinite phase space and potential unbounded from below

@article{Exner2011SpectralEF,
  title={Spectral estimates for a class of Schr\"odinger operators with infinite phase space and potential unbounded from below},
  author={P. Exner and Diana Barseghyan},
  journal={arXiv: Mathematical Physics},
  year={2011}
}
  • P. Exner, Diana Barseghyan
  • Published 2011
  • Physics, Mathematics
  • arXiv: Mathematical Physics
  • We analyze two-dimensional Schr\"odinger operators with the potential $|xy|^p - \lambda (x^2+y^2)^{p/(p+2)}$ where $p\ge 1$ and $\lambda\ge 0$. We show that there is a critical value of $\lambda$ such that the spectrum for $\lambda \lambda_\mathrm{crit}$ it is unbounded from below. In the subcritical case we prove upper and lower bounds for the eigenvalue sums. 

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