Show for a general potential energy V(r) that the form of the spin-orbit Hamiltonian (11.78) becomes H5-0 = 2m2c f| dr Suggestion: Start with (11.77). In order to determine the form of the spin-orbit interaction, we sart wiui a classical argument. In the rest frame of the electron, the motion of the proton generate, current, which, from the Biot-Savart law, produces a magnetic field -Zev x r (11.75) cr3 where-v is the proton's velocity, which is equal and opposite to the velocity v of the electron in the proton's rest frame. The energy of interaction of the electron's intrinsic spin magnetic moment with this magnetic field is given by - Zev xr c r3 Ze? ge S. 2m c - L - B = . S-L (11.76) %3D m2c2r3 where L=r xp is the electron's orbital angular momentum. We have also taken g = 2 for the electron. Equation (11.76) might not seem like a truly relativistic effect. However, we can express the magnetic field (11.75) as B = -(v/c) x E (11.77)