On Schrödinger operators with ${\delta }^{\prime }$-potentials supported on star graphs

Abstract

The spectral properties of two-dimensional Schrödinger operators with ${\delta }^{\prime }$-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.

arXiv comment20 pages. A slightly revised version is published in J. Phys. A

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