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7.1.3 H3' = $ {\pi \hbar ^2 \over 2 m^2 c^2}$$ \left(\vphantom{ {Ze^2 \over 4 \pi \varepsilon _0} }\right.$$ {Ze^2 \over 4 \pi \varepsilon _0}$ $ \left.\vphantom{ {Ze^2 \over 4 \pi \varepsilon _0} }\right)$$ \delta$($ \vec{r}\,$) (Darwin-Term)


$\displaystyle \Delta$E3 = $\displaystyle {\pi \hbar^2 \over 2 m^2 c^2}$$\displaystyle {Ze^2 \over 4 \pi \varepsilon_0}$$\displaystyle \langle$$\displaystyle \psi_{n00}^{}$|$\displaystyle \delta$(r)|$\displaystyle \psi_{n00}^{}$ =     (187)
$\displaystyle {\pi \hbar^2 \over 2 m^2 c^2}$$\displaystyle {Ze^2 \over 4 \pi \varepsilon_0}$|$\displaystyle \psi_{n00}^{}$|2     (188)
= - En$\displaystyle {Z\alpha^2 \over n}$     (189)


Alexander Wagner
2000-04-15