Geodesic
On the discrete spectrum of a quantum waveguide with Neumann windows in presence of exterior field
Nanosistemy: fizika, himiâ, matematika, Tome 13 (2022) no. 2, pp. 156-163.

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The discrete spectrum of the Hamiltonian describing a quantum particle living in three dimensional straight layer of width $d$ in the presence of a constant electric field of strength $F$ is studied. The Neumann boundary conditions are imposed on a finite set of bounded domains (windows) posed at one of the boundary planes and the Dirichlet boundary conditions on the remaining part of the boundary (it is a reduced problem for two identical coupled layers with symmetric electric field). It is proved that such system has eigenvalues below the lower bound of the essential spectrum for any $F\ge0$. Then we closer examine a dependence of bound state energies on $F$ and window's parameters, using numerical methods.
Keywords: quantum waveguide, Schrödinger operator, discrete spectrum. 
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     author = {A. S. Bagmutov and H. Najar and I. F. Melikhov and I. Y. Popov},
     title = {On the discrete spectrum of a quantum waveguide with {Neumann} windows in presence of exterior field},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {156--163},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2022_13_2_a3/}
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A. S. Bagmutov; H. Najar; I. F. Melikhov; I. Y. Popov. On the discrete spectrum of a quantum waveguide with Neumann windows in presence of exterior field. Nanosistemy: fizika, himiâ, matematika, Tome 13 (2022) no. 2, pp. 156-163. http://geodesic.mathdoc.fr/item/NANO_2022_13_2_a3/