We have solved the problem of a non-relativistic, spinless electron in a coulomb potential exactly. Real Hydrogen atoms have several small corrections to this simple solution. If we say that electron spin is a relativistic effect, they can all be called relativistic corrections which are off order compared to the Hydrogen energies we have calculated.
fine structure effects
and summing them we find that we get a nice cancellation yielding a simple formula.
We also compute the Zeeman effect in which an external magnetic field is applied to Hydrogen. The external field is very important since it breaks the spherical symmetry and splits degenerate states allowing us to understand Hydrogen through spectroscopy.
The correction due to a weak magnetic field is found to be
In the strong field limit we could use states of definite and and calculate the effects of the fine structure, , as a perturbation. In an intermediate strength field, on the order of 500 Gauss, the combination of the Hydrogen fine structure Hamiltonian and the term to the B field must be diagonalized on the set of states with the same principal quantum number .
Jim Branson 2013-04-22