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. 11431151. ISSN 00029939. http://resolver.caltech.edu/CaltechAUTHORS:20111012100552340

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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)lnxy+C_2^2 dx dy where C_1 = 1/2π and C_2 = (ln2γ)/2π (γ is the Euler constant). This estimate holds for all potentials for which the previous integral is finite.
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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 onedimensional 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:20111012100552340  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20111012100552340  
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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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