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%
% anharmonisch.tex -- Potential einer anharmonischen Schwingung
%
% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
%
\documentclass[tikz]{standalone}
\usepackage{amsmath}
\usepackage{times}
\usepackage{txfonts}
\usepackage{pgfplots}
\usepackage{csvsimple}
\usetikzlibrary{arrows,intersections,math}
\begin{document}
\def\skala{1}
\definecolor{darkgreen}{rgb}{0,0.6,0}
\begin{tikzpicture}[>=latex,thick,scale=\skala]
\def\E{3}
\def\K{0.2}
\def\D{0.0025}
\pgfmathparse{sqrt(\K/\D)}
\xdef\xnull{\pgfmathresult}
\pgfmathparse{sqrt((\K+sqrt(\K*\K-4*\E*\D))/\D)}
\xdef\xplus{\pgfmathresult}
\pgfmathparse{sqrt((\K-sqrt(\K*\K-4*\E*\D))/\D)}
\xdef\xminus{\pgfmathresult}
\def\xmax{13}
\fill[color=darkgreen!20] (0,-1.5) rectangle (\xminus,4.7);
\node[color=darkgreen] at ({0.5*\xminus},4.7) [below] {anziehende Kraft\strut};
\fill[color=orange!20] (\xplus,-1.5) rectangle (\xmax,4.7);
\node[color=orange] at ({0.5*(\xplus+\xmax)},4.7) [below] {abstossende\strut};
\node[color=orange] at ({0.5*(\xplus+\xmax)},4.3) [below] {Kraft\strut};
\node[color=gray] at (\xnull,4.7) [below] {verbotener Bereich\strut};
\draw (-0.1,\E) -- (0.1,\E);
\node at (-0.1,\E) [left] {$E$};
\draw[color=red,line width=1pt]
plot[domain=0:13,samples=100]
({\x},{\E-(0.5*\K-0.25*\D*\x*\x)*\x*\x});
\draw[->] (-0.1,0) -- ({\xmax+0.3},0) coordinate[label={$x$}];
\draw[->] (0,-1.5) -- (0,5) coordinate[label={right:$f(x)$}];
\fill[color=blue] (\xminus,0) circle[radius=0.08];
\node[color=blue] at (\xminus,0) [below left] {$x_-\mathstrut$};
\fill[color=blue] (\xplus,0) circle[radius=0.08];
\node[color=blue] at (\xplus,0) [below right] {$x_+\mathstrut$};
\fill[color=blue] (\xnull,0) circle[radius=0.08];
\node[color=blue] at (\xnull,0) [below] {$x_0\mathstrut$};
\end{tikzpicture}
\end{document}
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