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Diffstat (limited to 'buch/papers/laguerre/wasserstoff.tex')
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diff --git a/buch/papers/laguerre/wasserstoff.tex b/buch/papers/laguerre/wasserstoff.tex new file mode 100644 index 0000000..caaa6af --- /dev/null +++ b/buch/papers/laguerre/wasserstoff.tex @@ -0,0 +1,29 @@ +% +% 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} |