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-%
-% wasserstoff.tex
-%
-% (c) 2022 Patrik Müller, Ostschweizer Fachhochschule
-%
-\section{Radialer Schwingungsanteil eines Wasserstoffatoms
-\label{laguerre:section:radial_h_atom}}
-
-\begin{align}
- \nonumber
- - \frac{\hbar^2}{2m}
- &
- \left(
- \frac{1}{r^2} \pdv{}{r}
- \left( r^2 \pdv{}{r} \right)
- +
- \frac{1}{r^2 \sin \vartheta} \pdv{}{\vartheta}
- \left( \sin \vartheta \pdv{}{\vartheta} \right)
- +
- \frac{1}{r^2 \sin^2 \vartheta} \pdv[2]{}{\varphi}
- \right)
- u(r, \vartheta, \varphi)
- \\
- & -
- \frac{e^2}{4 \pi \epsilon_0 r} u(r, \vartheta, \varphi)
- =
- E u(r, \vartheta, \varphi)
- \label{laguerre:pdg_h_atom}
-\end{align}