- 09-51 Oleg Safronov
- On a sum rule for Schr\"odinger operators with complex potentials
Mar 15, 09
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Abstract. We study the distribution of eigenvalues of the one-dimensional Schr\"odinger 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.