1. Fine Structure in One-Electron Atoms

In atoms with only one electron, such as hydrogen, the electronic Hamiltonian is dominated by its electrostatic attraction to the nucleus. If we solve the Schrödinger equation with this Hamiltonian we get 'zeroth-order' approximations to the wavefunctions of the electron and the corresponding energies. This picture of the hydrogen atom is known as 'gross structure'. However there are a number of smaller interactions, treatable with perturbation theory, that give small but measureable shifts in the energy levels (and hence atomic spectra). Those are known as fine structure.

The spin-orbit Interaction

Classically, orbiting charges possess a magnetic dipole moment , and this holds in quantum mechanics also. Slightly more surprisingly, the intrinsic angular momentum of particles due to spin gives them a magnetic moment; thus the 'spin-half' electron acts like a little magnet. Since it is orbiting the positively charged nucleus, it 'sees' a current, and hence a magnetic field.

To add:

• Spin-orbit hamiltonian and effect on levels (choice of eigenstates for perturbation calculation)
• Relativistic kinetic energy correction
• Unusual hydrogenic atoms eg Muonium
• Fine structure in many-electron atoms