If a particle is in an energy eigenstate, then it must also be in a superposition of both outside the barrier and inside the barrier. So, if we measure the particle to be outside the barrier, I wouldn't think you could say that particle passed through the barrier because it was never really entirely inside the barrier.
If, however, the particle's wavefunction was entirely inside the barrier, then it must be in a superposition of energy eigenstates. Which means that you can't say that the particle doesn't have enough energy to cross the barrier since its energy isn't well defined.
So, why do we say that quantum tunneling is when a particle passes through a barrier they wouldn't classically have enough energy to overcome?
