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 | References | Similar Articles | Additional Information

Abstract: We study the distribution of eigenvalues of the one-dimensional Schrödinger operator with a complex valued potential . We prove that if 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

Email:
osafrono@uncc.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-10-10248-2

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.