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Darwin term

This follows from the Dirac equation and is given by
$\displaystyle \hat{H}_{\rm Darwin} = \frac{-e\hbar^2}{8m^2c^2} \Delta \Phi({\bf r}),$     (3.4)

where \bgroup\color{col1}$ \Delta$\egroup is the Laplacian. For the Coulomb potential \bgroup\color{col1}$ \Phi({\bf r})=Ze/4\pi\varepsilon_0 r$\egroup one needs
$\displaystyle \Delta \frac{1}{r}=-4\pi \delta({\bf r})$     (3.5)

with the Dirac Delta function \bgroup\color{col1}$ \delta({\bf r})$\egroup in three dimensions.



Tobias Brandes 2005-04-26