High Energy Eigenfunctions of One-Dimensional Schrödinger Operators with Polynomial Potentials

被引：0
|
作者：
Alexandre Eremenko
Andrei Gabrielov
Boris Shapiro
机构：
[1] Purdue University,Department of Mathematics
[2] Stockholm University,Department of Mathematics
来源：
Computational Methods and Function Theory | 2008年 / 8卷 / 2期
关键词：
Eigenfunctions; -symmetry; Stokes phenomena; asymptotics; 34B05; 34L20; 34M40; 34M60;
D O I：
10.1007/BF03321702
中图分类号：
学科分类号：
摘要：
For a class of one-dimensional Schrödinger operators with polynomial potentials that includes Hermitian and PT-symmetric operators, we show that the zeros of scaled eigenfunctions have a limit distribution in the complex plane as the eigenvalues tend to infinity. This limit distribution depends only on the degree of the polynomial potential and on the boundary conditions.
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页码：513 / 529
页数：16
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