I am drawing a little sketch, where a line enters a circle, and three other lines come out. Above each line, there is to be a tittle sinusoidal curve (almost as if I used a construct like \node (a) edge node[auto] {Some caption} (b); which you can find on page 48, PGF manual 2.10); this illustrates what I have so far (code below):

My question is: How can I place a wiggly line such as there is on the left above the other 3 lines on the right? Especially the lines also going north and south east are troubling me. Furthermore: how can I get anchors around the middle node (potential) which are placed on a circle, so that my edges coming all have the same length?
So far: I achieved placing the line above the left edge by placing two empty nodes above it, and shifting one to the left on the x axis, and one to the right, and naming them:
\node[shape=coordinate] (arrow start) [left=of potential,xshift=-1cm] {}
edge [post] node[auto,above,name=wavestart,yshift=0.3cm,xshift=-0.7cm] {}
node[auto,above,name=waveend,yshift=0.3cm,xshift=0.7cm] {} (potential);
Afterwards I could connect those new nodes easily by just creating another edge between them and pathmorphing it:
\path (wavestart) edge[decorate,decoration={snake,amplitude=1.4mm, segment length=15pt}] (waveend);
All code:
\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{patterns,positioning,decorations.pathmorphing,arrows}
\begin{document}
\begin{tikzpicture}%
[post/.style={->,shorten >=1pt,>=stealth',semithick}]
\node[circle, draw=black, pattern color=gray,%
pattern=north east lines,label=below:$V(x)$,%
minimum size=1cm] (potential) {};
\node[shape=coordinate] [above right=of potential] (outgoing up) {};
\node[shape=coordinate] [right=of potential] (outgoing mid) {};
\node[shape=coordinate] [below right=of potential] (outgoing down) {};
\path (potential)
edge[post] (outgoing up)
edge[post] (outgoing mid)
edge[post] (outgoing down);
\node[shape=coordinate] (arrow start) [left=of potential,xshift=-1cm] {}
edge [post] node[auto,above,name=wavestart,yshift=0.3cm,xshift=-0.7cm] {}
node[auto,above,name=waveend,yshift=0.3cm,xshift=0.7cm] {} (potential);
\path (wavestart) edge[decorate,decoration={snake,amplitude=1.4mm, segment length=15pt}] (waveend);
\end{tikzpicture}
\end{document}

