The square of the wave function is the probability density. For example, in one dimension the probability of finding a particle between x and x + dx is the wave function squared at x. As the wave function changes this probability density will change. One can define a probability current which describes the flow of the probability density. If the probability of finding a particle in a volume is increasing, then the probability current is flowing into that volume. Similarly, if the probability of finding a particle in a volume is decreasing, then the probability current is leaving the volume.

By examining the continuity equation in both one dimension and three dimensions, we are able to identify the probability current. For a simple plane wave, the probability current is just the square of the wave function times the velocity of the wave, (hbar k)/m. For stationary states the probability current is conserved because the probability is not changing with time.