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

David Damanik and Gerald Teschl

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.

MSC2000: Primary 47B36, 81Q10; Secondary 39A11, 47B39
Keywords: Discrete Schrödinger operators, bound states, oscillation theory

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