Discrete spectrum for Schrodinger operators with oscillating decaying potentials

被引：4

作者：

Raikov, Georgi ^{[1
]}

机构：

[1] Pontificia Univ Catolica Chile, Fac Matemat, Ave Vicuna Mackenna 4860, Santiago, Chile

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2016年 / 438卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

Schrodinger operators; Oscillating decaying potentials; Discrete spectrum; ABSOLUTELY CONTINUOUS-SPECTRUM; BOUND-STATES;

D O I：

10.1016/j.jmaa.2016.02.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Schrodinger operator H(eta)w = -Delta + eta W, self-adjoint in L-2 (R-d), d >= 1. Here eta is a non-constant oscillating function, while W decays slowly and regularly at infinity. We study the asymptotic behaviour of the discrete spectrum of H(eta)w near the origin, and due to the irregular decay of eta W, we encounter some non-semiclassical phenomena. In particular, H(eta)w has less eigenvalues than suggested by the semiclassical intuition. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：551 / 564

页数：14

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