On a sum rule for Schrödinger operators with complex potentials

Details On a sum rule for Schrödinger operators with complex potentials On a sum rule for Schrödinger operators with complex potentials

2009-03-12

arxiv.org/abs/0903.2267v3

Physics

Mathematical Physics

Scientific paper

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.

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