Proc. Amer. Math. Soc. 135, 1123-1127 (2007) [DOI: 10.1090/S0002-9939-06-08550-9]
Bound States of Discrete Schrödinger Operators with Super-Critical Inverse Square Potentials
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.