Quantitative Bounds Versus Existence of Weakly Coupled Bound States for Schrödinger Type Operators

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...

Full description

Saved in:
Bibliographic Details
Published in:Annales Henri Poincaré 2023-03, Vol.24 (3), p.783-842
Main Authors: Hoang, Vu, Hundertmark, Dirk, Richter, Johanna, Vugalter, Semjon
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Dynamical Systems and Ergodic Theory
Elementary Particles
Mathematical and Computational Physics
Mathematical Methods in Physics
Operators (mathematics)
Physics
Physics and Astronomy
Quantum Field Theory
Quantum Physics
Relativity Theory
Theoretical
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 a natural semi-classical type bound on the number of bound states precisely in the situation when weakly coupled bound states exist not.
ISSN:1424-0637
1424-0661
DOI:10.1007/s00023-022-01228-3