1D Schrödinger operators with complex potentials
arXiv:1909.08454 · doi:10.1134/S1061920820010082
Abstract
We consider a Schrödinger operator with complex-valued potentials on the line. The operator has essential spectrum on the half-line plus eigenvalues (counted with algebraic multiplicity) in the complex plane without the positive half-line. We determine series of trace formulas. Here we have the new term: a singular measure, which is absent for real potentials. Moreover, we estimate of sum of Im part of eigenvalues plus singular measure in terms of the norm of potentials. The proof is based on classical results about the Hardy spaces.
arXiv admin note: text overlap with arXiv:1811.09252