3The concept of a transmission time for a wave packet is pre- cise only to the extent that the packet is sharp in k space. As an illuminating contrast, consider a packet impinging on a double barrier with two resonances of different lifetimes. For a packet broad enough in its energy distribution to cover both reso- nances, a characterization of the tunneling delay in terms of a single (average) transmission time is, if formally possible, not very meaningful from a physical point of view.
Explain footnote #3
In quantum mechanics, a wave packet represents a localized and finite waveform that can be used to describe the behavior of a quantum particle. The concept of transmission time refers to the time it takes for a wave packet to travel through a medium or barrier. However, the precision of this concept is limited by the sharpness of the wave packet in k space, where k represents the wave vector associated with the particle's momentum.
If the wave packet is broad in its energy distribution, it may cover multiple resonances of the medium or barrier it interacts with. In this case, the characterization of the tunneling delay in terms of a single average transmission time is not physically meaningful. This is because the wave packet experiences different transmission times through the different resonances, each with its own unique lifetime. Thus, the concept of a single transmission time is not sufficient to describe the behavior of the wave packet.
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