From 670555039265d83945b0d3e205aefb020425585b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Wed, 6 Apr 2022 08:00:09 +0200 Subject: Start definition.tex --- buch/papers/laguerre/images/wasserstoff_model.tex | 58 +++++++++++++++++++++++ 1 file changed, 58 insertions(+) create mode 100644 buch/papers/laguerre/images/wasserstoff_model.tex (limited to 'buch/papers/laguerre/images') diff --git a/buch/papers/laguerre/images/wasserstoff_model.tex b/buch/papers/laguerre/images/wasserstoff_model.tex new file mode 100644 index 0000000..fe838c3 --- /dev/null +++ b/buch/papers/laguerre/images/wasserstoff_model.tex @@ -0,0 +1,58 @@ +\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} \ No newline at end of file -- cgit v1.2.1 From b7ee1c1a6836f30d2267cfc9e6dbfa206b2cb737 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Thu, 12 May 2022 18:19:49 +0200 Subject: Derive Laguerre-Polynomials from Laguerre-ODE, proof orthogonality with Sturm-Liouville --- buch/papers/laguerre/images/laguerre_polynomes.pdf | Bin 0 -> 16239 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 buch/papers/laguerre/images/laguerre_polynomes.pdf (limited to 'buch/papers/laguerre/images') diff --git a/buch/papers/laguerre/images/laguerre_polynomes.pdf b/buch/papers/laguerre/images/laguerre_polynomes.pdf new file mode 100644 index 0000000..3976bc7 Binary files /dev/null and b/buch/papers/laguerre/images/laguerre_polynomes.pdf differ -- cgit v1.2.1 From 7397861ade0537bf8e501fa87bd57653d932d459 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Patrik=20M=C3=BCller?= Date: Thu, 12 May 2022 18:21:25 +0200 Subject: Remove deprecated files --- buch/papers/laguerre/images/wasserstoff_model.tex | 58 ----------------------- 1 file changed, 58 deletions(-) delete mode 100644 buch/papers/laguerre/images/wasserstoff_model.tex (limited to 'buch/papers/laguerre/images') diff --git a/buch/papers/laguerre/images/wasserstoff_model.tex b/buch/papers/laguerre/images/wasserstoff_model.tex deleted file mode 100644 index fe838c3..0000000 --- a/buch/papers/laguerre/images/wasserstoff_model.tex +++ /dev/null @@ -1,58 +0,0 @@ -\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} \ No newline at end of file -- cgit v1.2.1