On a sum rule for Schrödinger operators with complex potentials

Oleg Safronov

Published 2009-03-12, updated 2010-02-11Version 3

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.