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Semiclassical Eigenfunctions of the Schrödinger Operator on a Graph That Are Localized Near a Subgraph

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Abstract

We study semiclassical eigenvalues and eigenfunctions of the Schrödinger operator on a geometric graph. We show that nontrivial boundary conditions at vertices lead to the existence of eigenfunctions, concentrated near a single vertex. We also construct semiclassical eigenfunctions, localized near edges and discuss general construction of spectral series which correspond to a general subgraph.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, 119991, Moscow, Russia

    A. I. Shafarevich

  2. Ishlinsky Institure for Problems in Mechanics of the Russian Academy of Sciences, Prospekt Vernadskogo 101, Moscow, Russia

    A. I. Allilueva & A. I. Shafarevich

  3. Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region, Russia

    A. I. Allilueva & A. I. Shafarevich

  4. National Research Centre “Kurchatov Institute,”, Moscow, Russia

    A. I. Allilueva & A. I. Shafarevich

Authors
  1. A. I. Allilueva
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  2. A. I. Shafarevich
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Correspondence to A. I. Allilueva.

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Allilueva, A.I., Shafarevich, A.I. Semiclassical Eigenfunctions of the Schrödinger Operator on a Graph That Are Localized Near a Subgraph. Russ. J. Math. Phys. 25, 139–147 (2018). https://doi.org/10.1134/S1061920818020012

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  • DOI: https://doi.org/10.1134/S1061920818020012

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