1-D Quantum Mechanics Conceptual Problem

1. The problem statement, all variables and given/known data

The probability density at certain points for a particle in a box is zero. Does this imply that the particle cannot move across these points? Explain. (I found a picture online here).

2. Relevant equations

3. The attempt at a solution

In a particle in a box, you can graph |ψ|2 is the probability of finding a particle at a certain point in space. If you graph the function, there are nodes where the function is equal to zero. I know that this implies that you will never find the particle at that specific location, and I also understand that the particle can still cross that node. I just cannot figure out a proper, physical way to explain this. I know that the answer is that these zero probability points do not imply that the particle cannot move across the points, but I am having trouble explaining why.

Any help would be great,
Thank you.

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