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

共 50 条

[1] DISCRETE SCHRODINGER OPERATORS WITH DECAYING AND OSCILLATING POTENTIALS
Frank, R. L.
Larson, S.
ST PETERSBURG MATHEMATICAL JOURNAL, 2024, 35 (01) : 233 - 244
[2] Absolutely continuous spectrum of Schrodinger operators with slowly decaying and oscillating potentials
Laptev, A
Naboko, S
Safronov, O
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2005, 253 (03) : 611 - 631
[3] Absolutely continuous spectrum of discrete Schrodinger operators with slowly oscillating potentials
Kim, Ahyoung
Kiselev, Alexander
MATHEMATISCHE NACHRICHTEN, 2009, 282 (04) : 552 - 568
[4] The resonance spectrum of Schrodinger operators with rapidly decaying potentials
Stepin, S. A.
Tarasov, A. G.
SBORNIK MATHEMATICS, 2009, 200 (11-12) : 1847 - 1880
[5] Negative Spectrum of Schrodinger Operators with Rapidly Oscillating Potentials
Read, Larry
ANNALES HENRI POINCARE, 2025, 26 (01): : 81 - 97
[6] Schrodinger operators with slowly decaying potentials
Davies, EB
Nath, J
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2002, 148 (01) : 1 - 28
[7] Some Schrodinger operators with power-decaying potentials and pure point spectrum, II. The discrete case
Remling, C
HELVETICA PHYSICA ACTA, 1998, 71 (02): : 200 - 213
[8] Absolutely Continuous Spectrum of Schrödinger Operators with Slowly Decaying and Oscillating Potentials
A. Laptev
S. Naboko
O. Safronov
Communications in Mathematical Physics, 2005, 253 : 611 - 631
[9] Schrodinger operators with rapidly oscillating potentials
Sasaki, Itaru
INTEGRAL EQUATIONS AND OPERATOR THEORY, 2007, 58 (04) : 563 - 571
[10] On the discrete spectrum of Schrodinger operators with Ahlfors regular potentials in a strip
Karuhanga, Martin
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 475 (01) : 918 - 938

← 1 2 3 4 5 →