Discrete spectrum for Schrodinger operators with oscillating decaying potentials

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:438

Article

Raikov, Georgi¹ 

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

关键词: Schrodinger operators;    Oscillating decaying potentials;    Discrete spectrum;   

DOI  :  10.1016/j.jmaa.2016.02.005

来源: Elsevier

【 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.

【 授权许可】

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