Even though the probability current is mentioned in many textbooks on QM, it does not have any physical interpretation within the conventional "Copenhagen" interpretation of QM. Yet, it does play a physical role in some alternative interpretations such as the Bohmian interpretation (BI). In BI, particles have deterministic trajectories and the velocity of the particle at a given point is proportional to the value of the probability current at that point. If you consider a statistical ensemble of many such trajectories, the continuity equation explains why such trajectories are compatible with the fact that probability density of particle positions is proportional to |psi|^2. For some non-technical aspects of BI see e.g.mess1n said:I'm going over the continuity equation and I'm having some problems getting an intuitive grasp of probability current density. I can't get an idea of what it is. I know the equation, but I don't really know what it means. Could anyone help me out?
Cheers,
Andrew