English

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 δ\delta'-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.

Keywords

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

R2 v1 2026-06-24T12:13:40.729Z