The discrete spectrum of Schrödinger operators with $\delta$-type conditions on regular metric trees

• DOI: 10.4171/jst/202
• Publication Date: 2018-02-05T22:30:15Z
• Authors: Jia Zhao; Guoliang Shi; Jun Yan
• Keywords: Schrödinger's cat; Discrete spectrum

This paper deals with the spectral properties of self-adjoint Schrödinger operators L_{Q}=-D^{2}+Q \delta -type conditions on regular metric trees. Firstly, we prove that operator \mathcal{L}_{\delta,Q} given in this is if it lower semibounded. Then a necessary and sufficient condition for spectrum to be discrete. The an analog Molchanov's discreteness criteria. Finally, using theory deficiency indices get which ensures spectra general boundary