Concentration of Eigenfunctions of Schrödinger Operators

Autor: Boris Mityagin, Petr Siegl, Joe Viola
Rok vydání: 2022
Předmět:
Zdroj: Journal of Fourier Analysis and Applications. 28
ISSN: 1531-5851
1069-5869
DOI: 10.1007/s00041-022-09961-3
Popis: We consider the limit measures induced by the rescaled eigenfunctions of Schrödinger operators with even confining potentials. We show that the limit measure is supported on $$[-1,1]$$ [ - 1 , 1 ] and with the density proportional to $$(1-|x|^\beta )^{-1/2}$$ ( 1 - | x | β ) - 1 / 2 when the non-perturbed potential resembles $$|x|^\beta $$ | x | β , $$\beta >0$$ β > 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.
Databáze: OpenAIRE
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