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\documentclass{standalone}
\usepackage{pgfplots}
\usepackage{tikz-3dplot}
\tdplotsetmaincoords{60}{115}
\pgfplotsset{compat=newest}
\begin{document}
\newcommand{\drawcircle}[4]{
\shade[ball color=#3, opacity=#4] (#1) circle (#2 cm);
\tdplotsetrotatedcoords{0}{0}{0};
\draw[dashed, tdplot_rotated_coords, #3!40!black] (#1) circle (#2);
}
\begin{tikzpicture}[tdplot_main_coords, scale = 2]
\def\r{1.0}
\def\rp{0.2}
\def\rn{0.05}
\def\rvec{1.0}
\def\thetavec{45}
\def\phivec{60}
\coordinate (O) at (0, 0, 0);
\tdplotsetcoord{P}{\rvec}{\thetavec}{\phivec}
% Labels
\node[inner sep=1pt] at (0, -4.0*\rp, 1.0*\r) (plabel){Proton};
\draw (plabel) -- (O);
\node[inner sep=1pt] at (-0.*\r, 1.0*\r, 1.3*\r) (elabel){Elektron};
\draw (elabel) -- (P);
% Draw proton
\drawcircle{O}{\rp}{red}{1.0}
% Draw spherical coordinates of electron
\draw (O) -- node[anchor=north west, yshift=4pt]{$r$} (P);
\draw[dashed] (O) -- (Pxy);
\draw[dashed] (P) -- (Pxy);
\tdplotdrawarc{(O)}{0.6}{0}{\phivec}{anchor=north}{$\varphi$}
\tdplotsetthetaplanecoords{\phivec}
\tdplotdrawarc[tdplot_rotated_coords]{(0,0,0)}{0.5}{0}%
{\thetavec}{anchor=south west, xshift=-2pt, yshift=-2pt}{$\vartheta$}
% Draw electron
\drawcircle{P}{\rn}{blue}{1.0}
% Draw surrounding sphere
\drawcircle{O}{\r}{gray}{0.3}
% Draw cartesian coordinate system
\draw[-stealth, thick] (O) -- (1.8*\r,0,0) node[below left] {$x$};
\draw[-stealth, thick] (O) -- (0,1.3*\r,0) node[below right] {$y$};
\draw[-stealth, thick] (O) -- (0,0,1.3*\r) node[above] {$z$};
\end{tikzpicture}
\end{document}
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