Darwin and relativistic kinetic energy correction for hydrogen

[kraigandrews]

Homework Statement

Combine the Darwin correction with the relativistic kinetic energy correction for l=0 to show that the fine structure formula:

\DeltaE_{fs}= - \frac{(E^{(0)2}_{n})}{2mc^{2}}[\frac{4n}{j + 1/2}-3]

remains valid for l=0

Homework Equations

From a previous problem the Darwin hamiltionian is shown to affected only under s-states
where for any s-state the formula \frac{2}{na^{3/2}}\frac{1}{\sqrt{4\pi}}

The Attempt at a Solution

so I know for s-states j=1/2 and l=0 (obviously). Overall, I am unsure as to what to show here, meaing:

do I combine the correction for the darwin energy to the correctionn for kinetic energy and then just show that for l=0, j=1/2 the equation still remains valid?

Thanks.

 

[sean_mp]

Have you checked http://en.wikipedia.org/wiki/Fine_structure ?