How to draw this figure in tikz?

How to draw this figure in tikz... I have tried to draw this in Geogebra and I have exported the codes to tikz,

\definecolor{qqqqff}{rgb}{0,0,1}
\definecolor{cqcqcq}{rgb}{0.75,0.75,0.75}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
\draw[->,color=black] (-3,0) -- (6,0);
\foreach \x in {-3,-2,-1,1,2,3,4,5}
\draw[shift={(\x,0)},color=black] (0pt,2pt) -- (0pt,-2pt) node[below] {\footnotesize $\x$};
\draw[->,color=black] (0,-1) -- (0,4);
\foreach \y in {-1,1,2,3}
\draw[shift={(0,\y)},color=black] (2pt,0pt) -- (-2pt,0pt) node[left] {\footnotesize $\y$};
\draw[color=black] (0pt,-10pt) node[right] {\footnotesize $0$};
\clip(-3,-1) rectangle (6,4);
\draw (1.18,3.04) node[anchor=north west] {$1$};
\draw (0.46,3.78) node[anchor=north west] {$\psi_1(x)$};
\begin{scriptsize}
\fill [color=qqqqff] (-8.84,-6.44) circle (1.5pt);
\fill [color=qqqqff] (12.78,-6.44) circle (1.5pt);
\end{scriptsize}
\end{tikzpicture}

And the output is, Here, I could not find the curve, why?? Shouldn't I draw using the pen tool in Geogebra?

--

Here is my Geogebra drawn pic in png format. • Take a look at this tex.stackexchange.com/questions/79228/… – Very23 Dec 16 '15 at 15:17
• – Jake Dec 16 '15 at 15:26
• Its not gaussian curve. It is just a hand drawn curve for my explanation in my example. So, kindly dont use gaussian curve, tell me how I can get the hand drawn curve exactly as look as in the picture. – David Dec 16 '15 at 15:39
• There is no code to draw the curve in the fragment you posted. Also, the part in the scriptsize environment can be deleted as it has no effect on the output. – cfr Dec 16 '15 at 17:17
• Take some graph paper, draw your curve, copy as many coordinates as you can, then use \draw graph[smooth] coordinates{...}; – John Kormylo Dec 16 '15 at 19:04

Note: since the OP mentions in the comments that the curves have no explicit mathematical functions and the aim is merely to mimic the curves, this is my attempt to solve it.

Caution: this solution is not good, not optimized, ..., etc. I've done it for fun. In this link, @Henri Menke has proposed a solution which is irrelevant to your problem based on trial and error. Basically, you upload your curves and draw on them. Let's say you want to mimic the below picture which is the second curve in your question. Now I will upload the picture and draw on it. Now we remove the original picture, the result is This is the code

\documentclass[border={2}]{standalone}
\usepackage{graphicx,tikz}

\begin{document}

\begin{tikzpicture}
\node[anchor=south west,inner sep=0] at (0,0)  {\includegraphics[width=\textwidth]{Capture.png}};
\draw[ultra thick,red,->] (.4,1.32) -- (11,1.32) node[anchor= west] {\Large $x$};
\draw[ultra thick,red,->] (5.72,0.1) -- (5.72,5.3) node[anchor= west] {\Large $\psi_{2}(x)$};
\draw[ultra thick,red] (5.1,3.7) node[left] {\Large 1} -- (5.72,3.7) ;

\draw[very thick,red] (1.8,1.32) to [out=10,in=225,looseness=1.2] (5.72,3.7);
\draw[very thick,red] (5.72,3.7) to [out=55,in=180,looseness=1.0] (7.0,4.5);
\draw[very thick,red] (7.0,4.5) to [out=0, in=132,looseness=0.9] (9.0,3.0);
\draw[very thick,red] (9.0,3.0) to [out=305, in=145,looseness=1.] (10.65,1.32);
\end{tikzpicture}

\end{document}

The result is ready to be shipped. :)

• I am sorry.. I dont understand how to draw ont it.. Can you explain how to tracing that pic?@croco – David Dec 18 '15 at 6:48
• @David, are you acquainted with Tikz? – CroCo Dec 18 '15 at 6:52
• somewhat... but I want to know that whether you are doing by putting helplines and marking them by finding the co-ordinates or is there any tracing tool in tikz??@croco – David Dec 18 '15 at 9:24