Bound states of discrete Schrödinger operators with super-critical inverse square potentials

Abstract

We consider discrete one-dimensional Schrödinger 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.

Identifiers

DOI

10.1090/s0002-9939-06-08550-9

Citations and references