I'm trying to plot some eigenfunctions (for a semicircle) in Mathematica. Functions are of the following form:
$$g_{ms}=J_{2m+1}(y_{ms}x) \sin ((2m+1)\varphi)$$
For example, for $m=0$ and $s=1$ it should look like what I drew by hand in the attached picture - something semicircular (sorry for bad drawing):
Well, I don't have much experience with Mathematica and the "code" I wrote so far doesn't give me the right result. Here's my try:
m = 0;
s = 1;
dat =
Table[
{x = RandomReal[{-1, 1}], y = RandomReal[{0, 1}],
BesselJ[(2*m + 1), BesselJZero[m, s]*x]* Sin[(2*m + 1)*ArcTan[x, y]]},
{1000}];
ListContourPlot[dat]
The plot I get is like this (see below). What am I doing wrong?
This is what I should get:
Edit: Thank you all. Now I use this code:
m = 1;
s = 1;
z = 2 m + 1;
ContourPlot[
BesselJ[z, BesselJZero[m, s]*Norm[{x, y}]]*
Sin[z*ArcTan[x, y]], {x, -5, 5}, {y, 0, 5}, Contours -> 10]
And I've got this plot:
Just another question - The repeating pattern doesn't end at x=1, as it does in the image from instructions. Did I mess something up with the code or do I just have to normalize it somehow?