I understand how to derive the probability current from the continuity equation and probability density. I was able to follow the proof at the beginning of http://www.youtube.com/watch?v=NSi27LC6plE" lecture perfectly. However, now I'm wondering, what if we were to prove the probability density from the continuity equation and the equation for probability current? To do so we would need to derive the probability current in a similar way the wave function, and probability density, for a particles position was derived. My question is, does it make sense to start with deriving the probability current and then use the continuity equation to derive the probability density? I thought about this and tried to figure out where I would start but drew a blank.