On a sum rule for Schrödinger operators with complex potentials
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- by Oleg Safronov PDF
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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 $|V|$ decays faster than the Coulomb potential, then the series of imaginary parts of square roots of eigenvalues is convergent.References
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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
- MR Author ID: 607478
- Email: osafrono@uncc.edu
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 2107-2112
- MSC (2000): Primary 47F05
- DOI: https://doi.org/10.1090/S0002-9939-10-10248-2
- MathSciNet review: 2596049