QM: Standing Wave Wavefunction and Probability I am going through the potential stepfunction and the resultant wavefunction of the particle as depicted below.

Lets assume a particle coming from left, and the calculation shows that incoming and reflected wavefunctions create a standing wave and the probablity in the region $x<0$ looks like below:

Now this is interesting, the probability. The nodes are fixed and does not change with time, and nodes represent zero probability of finding the particle. So physically does it mean if I send a particle, it gets confined (oscillate) between two subsequent nodes (!!), as it can't cross a node, as that would violate zero probability. But this is hard for me to imagine. Because if this is the case, then the particle will stop just at the left-node of the potential step-function and will oscillate between potential wall and the left-node!!!!
What am I getting wrong here?
 A: The issue that you are having is that there is no concept of a trajectory in quantum mechanics.
The wave function of the particle changes and at some point we measure the location of the particle and find it at some point.
This fundamentally changes the wave function.
If we stop measuring the wave function will again spread out and then measuring at a later time we will find the particle again at another point.
At no point does this require the particle to 'move through' a point where $|\Psi|^2 = 0$ as the particle isn't at a location unless we measure its position.
Remember that the position of the particle is also uncertain if we know anything about the momentum (and we do as we know the wave vector, $\mathbf{k} = \mathbf{p}/\hbar$).
A: The particle is cominging in and reflecting without caring about the nodes. They do not relate to where the particle actually is. They only describe where the particle can be and cannot be found when you make a measurement.
Quantum  measurements are not telling us what the particle is actually doing.
We know from the Bell inequalities  that there is  no local reality that is being measured.
A: The particle doesn't have a trajectory before measurement, so your statement that particles can't cross nodes is incorrect.The nodes are just $0$ probability. That's it. It doesn't mean you get particles oscillating (which also assumes a trajectory before measurement).
As a simpler example, the wave functions for states of definite energy for the particle in a box have nodes, but we do not say this means the particle is confined to only one section of the box between nodes.
