# Probability Current Density

1. May 31, 2010

### mess1n

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

2. May 31, 2010

### Demystifier

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.
http://xxx.lanl.gov/abs/physics/0702069 [Am.J.Phys.76:143-146,2008]
and references therein.