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Two-electron Atoms and Ions

Here, we deal with the Helium atom ( $\bgroup\color{col1}$ Z=2$\egroup$ ) , Lithium ion Li $\bgroup\color{col1}$ ^+$\egroup$ ( $\bgroup\color{col1}$ Z=3$\egroup$ ), Beryllium ion Be $\bgroup\color{col1}$ ^{++}$\egroup$ ( $\bgroup\color{col1}$ Z=4$\egroup$ ) etc. These are two-electron systems as in section III.2.1 with Hamiltonian Eq. (III.2.17),

$\displaystyle \hat{H}$	$\displaystyle =$	$\displaystyle -\frac{\hbar^2}{2m}\Delta_1+ V({\bf r}_1) -\frac{\hbar^2}{2m}\Delta_2 + V({\bf r}_2) + U\left(\vert{\bf r}_1 -{\bf r}_2\vert\right)$
$\displaystyle V({\bf r})$	$\displaystyle =$	$\displaystyle -\frac{Ze^2}{4\pi\varepsilon_0 r},\quad U\left(\vert{\bf r}_1 -{\... ...}_2\vert\right) = \frac{e^2}{4\pi\varepsilon_0 \vert{\bf r}_1 -{\bf r}_2\vert}.$	(3.1)

Subsections

Perturbation theory in $\bgroup\color{col1}$ U$\egroup$
- Ground state
- Excited states

Tobias Brandes 2005-04-26