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.
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| 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. | ||||||||||||
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| 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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