Proceedings of the American Mathematical Society

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On a sum rule for Schrödinger operators with complex potentials

Author: Oleg Safronov
Journal: Proc. Amer. Math. Soc. 138 (2010), 2107-2112
MSC (2000): Primary 47F05
Published electronically: January 22, 2010
MathSciNet review: 2596049
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Abstract: We study the distribution of eigenvalues of the one-dimensional Schrödinger operator with a complex valued potential $ V$. We prove that if $ \vert V\vert$ decays faster than the Coulomb potential, then the series of imaginary parts of square roots of eigenvalues is convergent.

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Additional Information

Oleg Safronov
Affiliation: Department of Mathematics, University of North Carolina, Charlotte, 9201 University City Boulevard, Charlotte, North Carolina 28223-0001

Keywords: Eigenvalue estimates, Schr\"odinger operators, complex potentials, sum rules
Received by editor(s): April 10, 2009
Received by editor(s) in revised form: October 4, 2009
Published electronically: January 22, 2010
Additional Notes: The author would like to thank B. Vainberg, S. Molchanov, A. Gordon and P. Grigoriev for inspiring and motivating discussions
Communicated by: Varghese Mathai
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.