najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2022-13-2-156-163najo-227Research ArticleСтатьиOn the discrete spectrum of a quantum waveguide with Neumann windows in presence of exterior fieldBagmutovA. S.bagmutov94@mail.ruNajarH. .hatemnajar@ipeim.rnu.tnMelikhovI. F.ivan.melikhov@gmail.comPopovI. Y.popov1955@gmail.comITMO UniversityRussian FederationFacultedes Sciences de MoanstirRussian Federation202206062025132156163Copyright © Bagmutov A.S., Najar H..., Melikhov I.F., Popov I.Y., 20252025Bagmutov A.S., Najar H..., Melikhov I.F., Popov I.Y.Bagmutov A.S., Najar H..., Melikhov I.F., Popov I.Y.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/227

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 ≥ 0. Then we closer examine a dependence of bound state energies on F and window’s parameters, using numerical methods.

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