Concentration of eigenfunctions of Schroedinger operators

Abstract

We consider the limit measures induced by the rescaled eigenfunctions of single-well Schrödinger operators. We show that the limit measure is supported on $[-1,1]$ and with the density proportional to $(1-|x{|}^{\beta }{)}^{-1/2}$ when the non-perturbed potential resembles $|x{|}^{\beta }$, $\beta >0$, for large $x$, and with the uniform density for super-polynomially growing potentials. We compare these results to analogous results in orthogonal polynomials and semiclassical defect measures.

24 pages, rewritten and extended

Cited by in corpus (1)

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