調和振動子の固有関数」です

\documentclass[border=10pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18} 
\begin{document}
\begin{tikzpicture}[nodes={font=\tiny}]
  \begin{axis}[
    hide axis, axis equal, thick,
    domain  = -4:4, samples = 100]
    \addplot[no markers] {2*exp(-1.1*x^2/2)};
    \addplot[no markers] {1.5*exp(-1.1*x^2/2)*-2.2*x+6};
    \addplot[no markers] {exp(-1.1*x^2/2)*(4*(-1.1*(x))^2-2)+12};
    \addplot[no markers] {0.6*exp(-1.01*x^2/2)*-1.1*(8 * \x^3 - 12 * \x)+20};
    \draw[dashed,thin] (axis cs:0,-4) -- (axis cs:0,26);
    \addplot[domain =-3:3] {(1.72*x)^2-2};
    \addplot[no markers, thin]  {0};% v=0
    \addplot[no markers, thin]  {6};% v=2
    \addplot[no markers, thin] {12};% v=2
    \addplot[no markers, thin] {20};% v=3
    \draw (axis cs:-6, 0) node {v=0};
    \draw (axis cs:-6, 6) node {v=1};
    \draw (axis cs:-6,12) node {v=2};
    \draw (axis cs:-6,20) node {v=3};
  \end{axis}
\end{tikzpicture}
\end{document}