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Spectra of Periodic Schrödinger Operators on the Degenerate Zigzag Nanotube with δ Type Vertex Conditions

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Abstract

In this paper, we consider the Schrödinger operators with a periodic potential and the δ type vertex conditions on a metric graph, which is called the degenerate zigzag nanotube, and discuss those spectrum. We demonstrate that the spectrum has the band structure. Moreover, we give the asymptotics of the band edges.

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Authors and Affiliations

  1. Maebashi Institute of Technology, 460-1 Kamisadori, Maebashi City, Gunma, 371-0816, Japan

    Hiroaki Niikuni

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  1. Hiroaki Niikuni
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Correspondence to Hiroaki Niikuni.

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This work is supported by Grant-in-Aid for Young Scientists B (2580085), Japan Society for Promotion of Science.

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Niikuni, H. Spectra of Periodic Schrödinger Operators on the Degenerate Zigzag Nanotube with δ Type Vertex Conditions. Integr. Equ. Oper. Theory 79, 477–505 (2014). https://doi.org/10.1007/s00020-014-2162-9

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  • DOI: https://doi.org/10.1007/s00020-014-2162-9

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