In analogy to the Poynting vector for EM radiation,
we may want to know the probability currentin some physical situation.
For example, in our free particle solution, the probability
density is uniform over all space, but there is a net flow
along the direction of the momentum.
The Flux of Probability *
derive an equation showing conservation of probability
and using the Schrödinger Equation.
This is the usual conservation equation if
is identified as the probability current.
This current can be computed from the wave function.
If we integrate if over some interval in
the equation says that the rate of change of probability in an interval is
equal to the probability flux into the integral minus the flux out.
Extending this analysis to 3 dimensions,