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.

arXiv comment24 pages, rewritten and extended

References in corpus (2)

• Differential operators admitting various rates of spectral projection growth
• Local form-subordination condition and Riesz basisness of root systems

Cited by in corpus (1)

• Generalised Airy Operators