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Schrödinger Operators with Few Bound States

Damanik, David and Killip, Rowan and Simon, Barry (2005) Schrödinger Operators with Few Bound States. Communications in Mathematical Physics, 258 (3). pp. 741-750. ISSN 0010-3616. doi:10.1007/s00220-005-1366-x. https://resolver.caltech.edu/CaltechAUTHORS:20170726-130636631

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s00220-005-1366-xDOIArticle
https://arxiv.org/abs/math-ph/0409074arXivDiscussion Paper
http://rdcu.be/uvNGPublisherFree ReadCube access
ORCID:
AuthorORCID
Damanik, David0000-0001-5924-3849
Killip, Rowan0000-0002-4272-7916
Simon, Barry0000-0003-2561-8539
Additional Information:© Springer-Verlag 2005. Received: 16 August 2004. Accepted: 28 January 2005. Published online: 2 June 2005. D. D. was supported in part by NSF grant DMS–0227289. R. K. was supported in part by NSF grant DMS–0401277. B. S. was supported in part by NSF grant DMS–0140592. It is our pleasure to thank Y. Pinchover and A. V. Sobolev for useful comments.
Funders:
Funding AgencyGrant Number
NSFDMS–0227289
NSFDMS–0401277
NSFDMS–0140592
Issue or Number:3
DOI:10.1007/s00220-005-1366-x
Record Number:CaltechAUTHORS:20170726-130636631
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170726-130636631
Official Citation:Damanik, D., Killip, R. & Simon, B. Commun. Math. Phys. (2005) 258: 741. https://doi.org/10.1007/s00220-005-1366-x
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79425
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:26 Jul 2017 21:38
Last Modified:15 Nov 2021 17:48

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