等厚势垒波导中的共振散射
Resonance scattering in a waveguide with identical thick barriers
摘要：
我们考虑波在任意有界横截面的无限波导中的传播，其内部被两个相同的带孔厚障碍物阻挡。当孔很小时，在很宽的频率范围内的波几乎被完全反射。然而，我们表明存在一个谐振频率，在该频率下，波几乎完全传输，即使是非常小的孔。这种共振散射在量子力学中被称为隧穿效应，与通常使用的抽象方法（如寻找散射矩阵的复值极点或非稳态散射理论）相比，这种共振散射通过相当基本的工具以建设性的方式被证明。特别是，我们推导出一个明确的方程，确定的谐振频率。所采用的基本工具，使非专家和教育吸引力的文件。
英文摘要：
We consider wave propagation across an infinite waveguide of an arbitrary bounded cross-section, whose interior is blocked by two identical thick barriers with holes. When the holes are small, the waves over a broad range of frequencies are almost fully reflected. However, we show the existence of a resonance frequency at which the wave is almost fully transmitted, even for very small holes. This resonance scattering, which is known as tunneling effect in quantum mechanics, is demonstrated in a constructive way by rather elementary tools, in contrast to commonly used abstract methods such as searching for complex-valued poles of the scattering matrix or non-stationary scattering theory. In particular, we derived an explicit equation that determines the resonance frequency. The employed elementary tools make the paper accessible to non-experts and educationally appealing.
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