The Darwin Term

We get a correction at the origin from the **Dirac equation**.

When we take the expectation value of this, we get the probability for the electron and proton to be at the same point.

Now,
for
and
for
, so

This is the same as term that we got for the spin orbit correction. This actually replaces the term in the spin-orbit correction (which should be zero) making the formula correct!

Jim Branson 2013-04-22