Abstract

By considering a quantum-mechanical system with complex eigenvalues, we show that indeed Levinson's theorem extends to the non self-adjoint setting. The perturbed system corresponds to a realization of the Schrodinger operator with inverse square potential on the half-line, while the Dirichlet Laplacian on the half-line is chosen for the reference system. The resulting relation is an equality between the number of eigenvalues of the perturbed system and the winding number of the scattering system together with additional operators living at 0-energy and at infinite energy. Published by AIP Publishing.