Returning to the pair of equations in
Note that for
, that is non-relativistic electrons,
is much bigger than
In the Hydrogen atom, would be of order
so we call
the large component and
the small component.
When we include relativistic corrections for the fine structure of Hydrogen, we must consider the effect
has on the normalization.
Remember that the conserved current indicates that the normalization condition for the four component Dirac spinor is.