From 403b8888ab0702f4d4cf4c7df24adc8c3fa45ab0 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Patrik=20M=C3=BCller?= <patrik.mueller@ost.ch>
Date: Mon, 7 Mar 2022 17:19:47 +0100
Subject: Start paper about Laguerre polynomials

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 buch/papers/laguerre/wasserstoff.tex | 29 +++++++++++++++++++++++++++++
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 create mode 100644 buch/papers/laguerre/wasserstoff.tex

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diff --git a/buch/papers/laguerre/wasserstoff.tex b/buch/papers/laguerre/wasserstoff.tex
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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}
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