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On the discrete spectrum of a quantum waveguide with Neumann windows in presence of exterior field
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On the discrete spectrum of a quantum waveguide with Neumann windows in presence of exterior field
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Journal Article
On the discrete spectrum of a quantum waveguide with Neumann windows in presence of exterior field
2022
Overview
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.
Publisher
St. Petersburg National Research University of Information Technologies, Mechanics and Optics
