I am trying to find Eigenvalues to a 12x12 Matrix ($H$) dependent on two variables $x$ and $y$. Later I want to do a 3D plot of one eigenvalue ($E$) over $x$ and $y$.
An analytical solution is not possible so what I calculate a Table
of numerical solutions and a ListPlot
:
Solution = Table[
Table[{x, y, N[Eigenvalue[H[x, y]]][[E]]}, {x, 0, 1}, {y, 0, 1}],
{E, 1, 12}
];
ListPlot3D[{Solution[[1]]}]
My Problem: apparently every time the eigenvalues to $H$ for a specific $x$ and $y$ is found, the order of eigenvalues is not the same as before. So if I do the ListPlot3D[{Solution[[1]]}]
I don't actually plot the eigenvalue 1 of $H$ but points of different eigenvalues of $H$.
So my question: How can I assign an order to my eigenvalues so that I know which value belongs to which eigenstate?
(Here you can find a link to the 12x12 matrix: http://pastebin.com/kUX4gdk8)