zero probability of the wavefunction for a particle in a finite space

[nSlavingBlair]

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

There was also 2 figures that go with it, but I don't know if it's possible to upload them. One shows psi against the length of the box and the other is |psi|^2 against the length of the box.

3. The attempt at a solution
There is no probability of the particle ever being at certain points within the box, which does not mean the particle gets stuck in one area of the box, but instead implies that the particle travels from one point to another without needing to occupy all intervening points.

As far as I can tell from my text book, this is a fairly acceptable answer. It just doesn't sit well for me. That would imply things like teleportation are possible. The only way I can imagine this to be possible is if, at those points, all the 'waves' that make up the particle cancel each other out, but I still don't like it as an explanation

Thank you for any help

[dx]

The particle doesn't have a position in the ordinary sense before you measure it. If you think about it as a classical particle with a position, and which moves at a certain speed, there is no way for it to move from one side of the zero-probability point to the other without spending a finite amount of time near the point itself, making the probability density finite there. You should think of the wave function as being the particle, and |\psi(x)|^2 as the probability density of finding it at x when you measure it.