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

Damanik, David; Teschl, Gerald

doi:10.1090/S0002-9939-06-08550-9

Bound states of discrete Schrödinger operators with super-critical inverse square potentials
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by David Damanik and Gerald Teschl

Proc. Amer. Math. Soc. 135 (2007), 1123-1127

DOI: https://doi.org/10.1090/S0002-9939-06-08550-9

Published electronically: October 4, 2006

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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.

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