Spectrum of Dirichlet Laplacian in a conical layer

Pavel Exner; Miloš Tater

doi:10.1088/1751-8113/43/47/474023

Spectrum of Dirichlet Laplacian in a conical layer

Mathematical Physics 2019-12-10 v2 math.MP Spectral Theory Quantum Physics

Authors: Pavel Exner , Miloš Tater

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Abstract

We study spectral properties of Dirichlet Laplacian on the conical layer of the opening angle $\pi-2\theta$ and thickness equal to $\pi$ . We demonstrate that below the continuum threshold which is equal to one there is an infinite sequence of isolated eigenvalues and analyze properties of these geometrically induced bound states. By numerical computation we find examples of the eigenfunctions.

Keywords

Dirichlet Laplacian conical layer spectrum bound states eigenvalues geometrically induced states

Cite

@article{arxiv.1006.0137,
  title  = {Spectrum of Dirichlet Laplacian in a conical layer},
  author = {Pavel Exner and Miloš Tater},
  journal= {arXiv preprint arXiv:1006.0137},
  year   = {2019}
}

Comments

With some improvements and a broader range of numerical results, to appear in J. Phys. A: Math. Theor

Spectrum of Dirichlet Laplacian in a conical layer

Abstract

Keywords

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