Author:
Hoang Vu,Hundertmark Dirk,Richter Johanna,Vugalter Semjon
Abstract
AbstractIt 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 a natural semi-classical type bound on the number of bound states precisely in the situation when weakly coupled bound states exist not.
Funder
Karlsruher Institut für Technologie (KIT)
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Nuclear and High Energy Physics,Statistical and Nonlinear Physics
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