High energy eigenfunctions of one-dimensional Schrodinger operators with polynomial potentials
Mathematical Physics
2008-08-08 v1 math.MP
Abstract
For a class of one-dimensional Schrodinger operators with polynomial potentials that includes Hermitian and PT-symmetric operators, we show that the zeros of scaled eigenfunctions have a limit disctibution in the complex plane as the eigenvalues tend to infinity. This limit distribution depends only on the degree of potential and on the boundary conditions.
Cite
@article{arxiv.math-ph/0703049,
title = {High energy eigenfunctions of one-dimensional Schrodinger operators with polynomial potentials},
author = {Alexandre Eremenko and Andrei Gabrielov and Boris Shapiro},
journal= {arXiv preprint arXiv:math-ph/0703049},
year = {2008}
}
Comments
22 pages, 9 figures