Abstract
In this chapter, we consider a three-dimensional waveguide that, far from the coordinate origin, coincides with a cylinder G containing the axis x. The cross-section of G is a two-dimensional domain (of an arbitrary form) with smooth boundary. The waveguide has two narrows of small diameter \(\varepsilon \). The waveguide part between the narrows plays the role of a resonator and there can arise conditions for electron resonant tunneling. We take \(\varepsilon \) as small parameter and obtain asymptotic formulas for characteristics of the resonant tunneling as \(\varepsilon \rightarrow 0\).
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