Spectral estimates for a class of Schrödinger operators with infinite phase space and potential unbounded from below
Abstract
We analyse twodimensional Schrödinger operators with the potential xy^{p}  λ(x^{2} + y^{2})^{p/(p + 2)} where p ⩾ 1 and λ ⩾ 0. We show that there is a critical value of λ such that the spectrum for λ < λ_{crit} is bounded below and purely discrete, while for λ > λ_{crit} it is unbounded from below. In the subcritical case, we prove upper and lower bounds for the eigenvalue sums.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 February 2012
 DOI:
 10.1088/17518113/45/7/075204
 arXiv:
 arXiv:1109.0168
 Bibcode:
 2012JPhA...45g5204E
 Keywords:

 Mathematical Physics;
 Mathematics  Spectral Theory;
 Quantum Physics;
 81Q10;
 35P15
 EPrint:
 LaTeX, 16 pages with on ps figure