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Zeitschrift für Analysis und ihre Anwendungen


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Volume 36, Issue 3, 2017, pp. 329–341
DOI: 10.4171/ZAA/1591

Published online: 2017-07-17

Examples of Plentiful Discrete Spectra in Infinite Spatial Cruciform Quantum Waveguides

Fedor L. Bakharev[1], Sergey G. Matveenko[2] and Sergei A. Nazarov[3]

(1) St. Petersburg State University, St. Petersburg, Russia
(2) St. Petersburg State University, and National Research University Higher School of Economics, St. Petersburg, Russia
(3) St. Petersburg State University and Institute for Problems of Mechanical Engineering, Saint Petersburg, Russia

Spatial cruciform quantum waveguides (the Dirichlet problem for Laplace operator) are constructed such that the total multiplicity of the discrete spectrum exceeds any preassigned number.

Keywords: Cruciform waveguide, multiplicity of discrete spectrum, asymptotics, localization of eigenfunctions, thin quantum lattices

Bakharev Fedor, Matveenko Sergey, Nazarov Sergei: Examples of Plentiful Discrete Spectra in Infinite Spatial Cruciform Quantum Waveguides. Z. Anal. Anwend. 36 (2017), 329-341. doi: 10.4171/ZAA/1591