On spectral estimates for two-dimensional Schrödinger operators (Q398179)

Summary: For the two-dimensional Schrödinger operator \(\mathrm{H}_{\alpha V}=-\Delta-\alpha V, V\geq 0\), we study the behavior of the number \(N_{-}(\mathrm{H}_{\alpha V})\) of its negative eigenvalues (bound states), as the coupling parameter \(\alpha\) tends to infinity. A wide class of potentials is described, for which \(N_{-}(\mathrm{H}_{\alpha V})\) has semi-classical behavior, i.e. \(N_{-}(\mathrm{H}_{\alpha V})=O(\alpha)\). For the potentials from this class, a necessary and sufficient condition is found for the validity of the Weyl asymptotic law.