1-D Quantum Mechanics Conceptual Problem

[Yosty22]

Homework Statement

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 http://www.everyscience.com/Chemistry/Physical/Quantum_Mechanics/.images/PBxWvfns1.gif).

Homework Equations

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.

 

[ehild]

If it helps, imagine the particle as if connected to a vibrating string. It spends the shortest time in the vicinity of the point where its speed the highest is. The probability that you find the particle there is the lowest.

ehild