To be used in future
 Chapter 6: Relativistic wave equations Up Chapter 6: Relativistic wave equations Section 6.2: Klein-Gordon equation 

6.1 Probability currents↓

Let us assume a Hamiltonian operator of the form If the wave function staisfies the Schrödinger equation, the probaility density satisfies the equation
↓This equation is called the “continuity equation” since it describes that the only way probably can disappear or appear in a finite volume, is by a flow of the probability current This is most easily understood by using Stokes theorem on the integral form of the continuity equation. Integrating Eq. (↓) over a volume with surface , we find that which shows exactly the rolw of probability and current stated above.
figure Figures/continuity.png
Figure 6.1 A graphical interpretation of the continuity equation: Loss of probability in the volume is due to the flow of the current perpendicular to the surface of the volume.
 Chapter 6: Relativistic wave equations Up Chapter 6: Relativistic wave equations Section 6.2: Klein-Gordon equation