In the case of a potential step when $E<V$, the transmission coefficient of the particle is zero. However, there is also an exponentially decaying wavefunction of the particle in that classically forbidden region. The existence of a finite valued wavefunction implies non-zero probability in that region.
So what exactly is the case? Is the probability of finding the particle on the other side of potential step exactly zero (as we see from transmission coefficient) or is it finite non-zero but very small (as is suggested by the non zero wavefunction)?
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