Probability Current Density

The continuity equation in QM is $\frac{\partial \rho}{\partial t} + \nabla \cdot \mathbf{J} = 0$, where: $$\mathbf{J} = \frac{\hbar}{2mi} (\Psi^* \nabla \Psi - \Psi \nabla \Psi^*)$$ This ensures the local conservation of probability.