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1) Why does the real part of the wave function collapse inside the barrier (square, rectangular, barrier with V less than the energy of particle)? It seems to me that there should be some probability that the particle, if tunneling, could get trapped inside the barrier, since as the wave collides with the barrier the wave function is non zero.

2) Is the wave function 'expanding' after 'collision' witht the barrier (for the reflected and transmitted waves) because the probability of it's position is changing? Has it lost momentum?

3) How is the real and imaginary components of the probability density dependant on time after the 'collision'? Is it more than just following the wave function? I understand that the amplitude is ever lowering due to the 'expansion' of the wave packets corresponding to the transmitted and reflected waves, but, not sure how each component are dependant on time.

I know these aren't great questions, but in my

*attempt*to understand the quantum world these few things are still bothering me.