Probability current density

[Abdul Quader]

In order to check if a quantum particle crosses a barrier or not, isn't calculating $|\psi(x)|^2$ enough in that particular region ? Why do we need to calculate probability current density for that matter?

 

[A. Neumaier]

It is not needed for this, and it is usually never computed. It is needed in the proof that probability is conserved unless it flows into or out of a boundary.