\documentclass{standalone}
\usepackage{mathtools}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
\draw [thin,->] (-.1,0)--(3,0) node[below]{$x$};
\draw [thin,->] (0,-1.1)--(0,4) ;






\draw[red] plot[domain=-.1:3,smooth] function {2/sqrt(pi)*(exp (-(x-1)**2) -exp (-(x+1)**2))};
\draw[green] plot[domain=-.1:3,smooth] function {1/sqrt(pi)*(exp (-(x-1)**2/4) -exp (-(x+1)**2/4))};

\draw[magenta] plot[domain=-.1:3,smooth] function {4/sqrt(pi)*(exp (-4*(x-1)**2) -exp (-4*(x+1)**2))};
\draw[blue] plot[domain=-.1:3,smooth] function {6/sqrt(pi)*(exp (-9*(x-1)**2) -exp (-9*(x+1)**2))};







\end{tikzpicture}
\end{document}



