1. Why is the (time independent) wavefunction an exponential decay inside the potential barrier? I know the mathematical derivation, but I am confused why traveling in a region with constant potential would cause the probability density to decrease.

2. When crossing from the finite barrier region to zero potential region, reflection still happens. Why is that happening? I think if I just take it for granted that it would happen, I can derive the wavefunction, but I am confused why it is happening.

3. When the initial kinetic energy is larger than the potential energy the particle would acquire in the barrier, neither reflection nor the exponential decay happens. At first, it is natural to me so I didn't think about it too much about it. But after thinking about the first 2 questions, I am starting to question why is this happening as well.