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A quantum particle, tunneling in a stationary potential, passes through a region with a weak slowly changing potential. Its probability density has resonances and oscillations in energy and in time, both in the barrier and beyond it. This is true in any dimensionality, for any type of waves (for example, de Broglie, electromagnetic, acoustic, and hydrodynamic waves).
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M. Ya. Azbel (1991) studied this question.
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