On the Negative Spectrum of One-Dimensional Schrödinger Operators with Point Interactions

Abstract

We investigate negative spectra of one-dimensional (1D) Schrodinger operators with δ- and δ′-interactions on a discrete set in the framework of a new approach. Namely, using the technique of boundary triplets and the corresponding Weyl functions, we complete and generalize the results of Albeverio and Nizhnik (Lett Math Phys 65:27–35, 2003; Methods Funct Anal Topol 9(4):273–286, 2003). For instance, we propose an algorithm for determining the number of negative squares of the operator with δ-interactions. We also show that the number of negative squares of the operator with δ′-interactions equals the number of negative strengths.