(2) Spin-orbit interaction Hamiltonian:

For a non-relativistic electron, i.e., an electron orbiting around a nucleus with an orbital velocity v_orbit much less than the speed of light in vacuum, or , the non-relativistic version of eqn.(6) can be derived by another way.

An observer sitting on the electron and moving with it thinks that the electron is at rest and the nucleus is revolving around it with a velocity . To the observer, the radius of the orbit will be and the nuclear charge will be +Ze. Consequently, according to the Biot-Savart's law, the magnetic flux density at the position of the electron will be given by