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arXiv · 2207.01617

On Schr\"odinger operators with $\delta'$-potentials supported on star graphs

Konstantin Pankrashkin·Marco Vogel
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Abstract

The spectral properties of two-dimensional Schr\"odinger operators with $\delta'$-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.

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Konstantin Pankrashkin, Marco Vogel. 2022-07-04. On Schr\"odinger operators with $\delta'$-potentials supported on star graphs. https://doi.org/10.1088/1751-8121%2Fac775a

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