Quantitative Bounds Versus Existence of Weakly Coupled Bound States for Schrödinger Type Operators
Quantitative Bounds Versus Existence of Weakly Coupled Bound States for Schrödinger Type Operators
Abstract It is well-known that for usual Schrödinger operators weakly coupled bound states exist in dimensions one and two, whereas in higher dimensions the famous Cwikel–Lieb–Rozenblum bound holds. We show for a large class of Schrödinger-type operators with general kinetic energies that these two phenomena are complementary. We explicitly get …