For the two-dimensional Schrödinger operator , we study the behavior of the number of its negative eigenvalues (bound states), as the coupling parameter tends to infinity. A wide class of potentials is described, for which has the semi-classical behavior, i.e. . For the potentials from this class, the necessary and sufficient condition is found for the validity of the Weyl asymptotic law.
Cite this article
Ari Laptev, Michael Solomyak, On spectral estimates for two-dimensional Schrödinger operators. J. Spectr. Theory 3 (2013), no. 4, pp. 505–515DOI 10.4171/JST/53