In a Tunneling problem, if the $E_o<V$, we can show that the scattering wavefunction inside a rectangular barrier is a decaying exponential. The solution being real implies that the probability current $J$ is zero at every point inside the barrier.
From equation of continuity,
Does this mean that the probability density at each point inside the barrier is fixed? (Clearly it can't be so). How exactly is this to be interpreted?