On Schr\"odinger operators with $\delta'$-potentials supported on star graphs
Spectral Theory
2022-07-05 v1 Mathematical Physics
math.MP
Abstract
The spectral properties of two-dimensional Schr\"odinger operators with -potentials supported on star graphs are discussed. We describe the essential spectrum and give a complete description of situations in which the discrete spectrum is non-trivial but finite. A more detailed study is presented for the case of a star graph with two branches, in particular, the small angle asymptotics for the eigenvalues is obtained.
Cite
@article{arxiv.2207.01617,
title = {On Schr\"odinger operators with $\delta'$-potentials supported on star graphs},
author = {Konstantin Pankrashkin and Marco Vogel},
journal= {arXiv preprint arXiv:2207.01617},
year = {2022}
}
Comments
20 pages. A slightly revised version is published in J. Phys. A