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arXiv · 1208.3072

Trace Formulae for quantum graphs with edge potentials

Ralf Rueckriemen·Uzy Smilansky
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Abstract

This work explores the spectra of quantum graphs where the Schr\"odinger operator on the edges is equipped with a potential. The scattering approach, which was originally introduced for the potential free case, is extended to this case and used to derive a secular function whose zeros coincide with the eigenvalue spectrum. Exact trace formulas for both smooth and $\delta$-potentials are derived, and an asymptotic semiclassical trace formula (for smooth potentials) is presented and discussed.

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Ralf Rueckriemen, Uzy Smilansky. 2012-08-15. Trace Formulae for quantum graphs with edge potentials. https://doi.org/10.1088/1751-8113/45/47/475205

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