Stoiciu, Mihai (2004) An estimate for the number of bound states of the Schrödinger operator in two dimensions. Proceedings of the American Mathematical Society, 132 (4). pp. 1143-1151. ISSN 0002-9939 http://resolver.caltech.edu/CaltechAUTHORS:20111012-100552340
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Abstract
For the Schrödinger operator -Δ + V on R^2 be the number of bound states. One obtains the following estimate: N(V) ≤ 1 + ∫_(R^2)∫_(R^2)|V(x)|V(y)|C_(1)ln|x-y|+C_2|^2 dx dy where C_1 = -1/2π and C_2 = (ln2-γ)/2π (γ is the Euler constant). This estimate holds for all potentials for which the previous integral is finite.
| Item Type: | Article | ||||
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| Additional Information: | © 2003 American Mathematical Society. Received by editor(s): December 17, 2002; Posted: August 28, 2003; Communicated by: Joseph A. Ball. I would like to thank B. Simon for proposing the problem and both R. Killip and B. Simon for useful discussions. Note added in proof: After the submission of this paper I learned of further related results: N. Setô [15], R. Newton [14] and M. Solomyak [17]. Readers interested in the one-dimensional problem should refer to B. Simon [16] and M. Klaus [13]. I would like to thank P. Exner for bringing some of these papers to my attention. | ||||
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| Classification Code: | MSC (2000): Primary 35P15, 35J10; Secondary 81Q10 | ||||
| Record Number: | CaltechAUTHORS:20111012-100552340 | ||||
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20111012-100552340 | ||||
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| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||
| ID Code: | 27181 | ||||
| Collection: | CaltechAUTHORS | ||||
| Deposited By: | Jason Perez | ||||
| Deposited On: | 12 Oct 2011 20:03 | ||||
| Last Modified: | 26 Dec 2012 14:15 |
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