The full dirac equation predicts anti-particles. It is written in terms of bi-spinors which are a spinor for a particle and a spinor for the anti-particle. . For lower energies, the dirac equation can just be written in terms of 2 spinors, rather than a bispinor.

In an external magnetic field this leads to This energy is really .

After expanding in powers of , you get:

The first term has ordinary zeeman effect. Second term is anomalous zeeman effect. Third term is relativistic mass correction. 4th term is Darwin term. 5th term is spin-orbit coupling. The last term is typically expanded in multipoles and produces the stark effect.y

source psfile jl@crush.caltech.edu index