On a sum rule for Schrödinger operators with complex potentials

2009/03/12 by Safronov, Oleg
#47F05 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.0903.2267

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.

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