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

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

2005-09-05

arxiv.org/abs/math/0509110v1

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

Mathematics

Spectral Theory

4 pages

Scientific paper

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.

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