An estimate for the number of bound states of the Schrödinger operator in two dimensions
Author:
Mihai Stoiciu
Journal:
Proc. Amer. Math. Soc. 132 (2004), 11431151
MSC (2000):
Primary 35P15, 35J10; Secondary 81Q10
Published electronically:
August 28, 2003
MathSciNet review:
2045431
Fulltext PDF Free Access
Abstract 
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Additional Information
Abstract: For the Schrödinger operator on let be the number of bound states. One obtains the following estimate:
where and ( is the Euler constant). This estimate holds for all potentials for which the previous integral is finite.
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 M. Reed and B. Simon, Methods of Modern Mathematical Physics, II: Fourier Analysis, Self Adjointness, Academic Press, New York, 1975. MR 58:12429b
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 B. Simon, On the number of bound states of twobody Schrödinger operators: A review, in Studies in Mathematical Physics, Essays in Honor of Valentine Bargmann, Princeton University Press, Princeton, 1976, pp. 305326.
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 M. Klaus, On the bound state of Schrödinger operators in one dimension, Ann. Physics 108 (1977), no. 2, 288300. MR 58:20010
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Additional Information
Mihai Stoiciu
Affiliation:
Department of Mathematics 25337, California Institute of Technology, Pasadena, California 91125
Email:
mihai@its.caltech.edu
DOI:
http://dx.doi.org/10.1090/S0002993903072575
PII:
S 00029939(03)072575
Received by editor(s):
December 17, 2002
Published electronically:
August 28, 2003
Communicated by:
Joseph A. Ball
Article copyright:
© Copyright 2003 American Mathematical Society
