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The fine structure is a result of relativistic corrections to the Schrödinger equation, derived from the relativistic Dirac equation for an electron of mass
and charge
in an external electrical field
. Performing an expansion in
, where
is the velocity of the electron and
is the speed of light, the result for the Hamiltonian
can be written as
,
where
|
|
|
(3.1) |
is the non-relativistic Hydrogen atom, (
), cf. Eq. (II.1.7), and
is treated as a
perturbation to
, using perturbation theory.
consists of three terms: the kinetic energy correction, the Darwin term, and the Spin-Orbit coupling,
|
|
|
(3.2) |
Literature: Gasiorowicz [3] cp. 12 (Kinetic Energy Correction, Spin-Orbit coupling); Weissbluth [4] (Dirac equation, Darwin term); Landau Lifshitz Vol IV chapter. 33,34.
Subsections
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Tobias Brandes
2005-04-26