Schrödinger Operators with Few Bound States

被引：0
作者：
David Damanik
Rowan Killip
Barry Simon
机构：
[1] Mathematics 253–37,Department of Mathematics
[2] California Institute of Technology,undefined
[3] University of California,undefined
来源：
Communications in Mathematical Physics | 2005年 / 258卷
关键词：
Neural Network; Statistical Physic; Complex System; Nonlinear Dynamics; Potential Versus;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We show that whole-line Schrödinger operators with finitely many bound states have no embedded singular spectrum. In contradistinction, we show that embedded singular spectrum is possible even when the bound states approach the essential spectrum exponentially fast. We also prove the following result for one- and two-dimensional Schrödinger operators, H, with bounded positive ground states: Given a potential V, if both H±V are bounded from below by the ground-state energy of H, then V≡0.
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页码：741 / 750
页数：9
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