Given a particle travelling very close to the speed of light encountering a barrier, is it possible for the particle to exceed the speed of light by tunnelling forward in the direction of motion through the barrier?
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Here is the simple quantum mechanical barrier tunneling situation:
According to classical physics, a particle of energy E less than the height U0 of a barrier could not penetrate - the region inside the barrier is classically forbidden. But the wavefunction associated with a free particle must be continuous at the barrier and will show an exponential decay inside the barrier. The wavefunction must also be continuous on the far side of the barrier, so there is a finite probability that the particle will tunnel through the barrier.
etc.
The impotant thing to keep in mind is that the energy level is the same inside and outside the barrier, thus the particle must have the same momentum i.e. velocity all through. It is only the probabilities that change, because this is a quantum mechanical phenomenon.
A particle moving near the velocity of light and hitting a barrier, may radiate Cerenkov radiation entering the medium, and thus reduce its energy, but that is another story, not tunneling, itis scattering.
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