Complex eigenvalue bounds for a Schrödinger operator on the half line

Abstract

We derive some bounds on the location of complex eigenvalues for a family of Schrödinger operators $H_{0,\nu }$ defined on the positive half line and subject to integrable complex potential. We generalise the results obtained in [14] where the operator does not have a Hardy term and also include the analysis for potentials belonging to weighted $L^p$ spaces. Some information on the geometry of the complex region which bounds the eigenvalues of the radial Schrödinger multidimensional operator are then recovered.