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Article
On the Embedded Eigenvalues and Dense Point Spectrum of the Stark-Like Hamiltonians
Article first published online: 11 NOV 2006
DOI: 10.1002/mana.19971830112
Copyright © 1997 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1522-2616/asset/cover.gif?v=1&s=0110fef2c1f789362b0c8808bc8248840b71170f "Mathematische Nachrichten")
Additional Information
How to Cite
Naboko, S. N. and Pushnitski, A. B. (1997), On the Embedded Eigenvalues and Dense Point Spectrum of the Stark-Like Hamiltonians. Math. Nachr., 183: 185–200. doi: 10.1002/mana.19971830112
Publication History
- Issue published online: 11 NOV 2006
- Article first published online: 11 NOV 2006
- Manuscript Received: 16 JAN 1995
- Abstract
- References
- Cited By
Keywords:
- Schrödinger operators;
- Stark operators;
- embedded eigenvalues
Abstract
The point spectrum lying on the essential spectrum is investigated for the one-dimensional Schrödinger operator 
with decaying potential q, and weakly perturbed Stark-like operator 
An elementary constructive technique is developed to obtain various results concerning embedded eigenvalues of Schrödinger operators. In Section 3 a constructive example of the Stark - like operator with the potential q decaying slightly slowlier than o(1/|x|1-α/2)and dense point spectrum on the whole real axis is presented.