Bound States of Discrete Schroedinger Operators with Super-Critical Inverse Square Potentials

Abstract

We consider discrete one-dimensional Schroedinger operators whose potentials decay asymptotically like an inverse square. In the super-critical case, where there are infinitely many discrete eigenvalues, we compute precise asymptotics of the number of eigenvalues below a given energy E as this energy tends to the bottom of the essential spectrum.

4 pages

References in corpus (3)

• Variational Estimates for Discrete Schrödinger Operators with Potentials of Indefinite Sign
• Schroedinger Operators With Few Bound States
• Schrödinger Operators with Many Bound States

Cited by in corpus (4)

• Bounds on the Discrete Spectrum of Lattice Schrödinger Operators
• On the bound states of the discrete Schrödinger equation with compactly supported potentials
• Darboux transformation for the discrete Schrödinger equation
• Bound states of discrete Schrödinger operators on one and two dimensional lattices