Fine structure#Darwin term

The Darwin term ( after Charles Galton Darwin) is a relativistic correction term in the Hamiltonian to explain the fine structure of the hydrogen spectrum theoretically.

It describes that the electrostatic interaction with the electric field of the electron of the core due to the dither motion is no longer locally in non- relativistic approximation, but also on a small area of the electric field to the electron around:

When the potential V is a Coulomb potential, the Darwin term can also be written as

It is

• The reduced Planck 's constant
• The electron mass
• The velocity of light
• : Laplace operator
• : The potential
• : The elementary charge
• The atomic number
• The delta function in three dimensions.

The electron is therefore not precisely located, its position fluctuates around, the Compton wavelength of the electron (multiplied by ).