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

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

2009-03-06

arxiv.org/abs/0903.1180v5

Mathematics

Spectral Theory

14 pages

Scientific paper

We investigate negative spectra of 1--D Schr\"odinger operators with $\delta$- and $\delta'$-interactions on a discrete set in the framework of a new approach. Namely, using technique of boundary triplets and the corresponding Weyl functions, we complete and generalize the results of S. Albeverio and L. Nizhnik. For instance, we propose the algorithm for determining the number of negative squares of the operator with $\delta$-interactions. We also show that the number of negative squares of the operator with $\delta'$-interactions equals the number of negative strengths.

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