You have to start somewhere and so far SL has been solely focussed on the solution of the 1D Schrödinger Eqn. In the next update I'm considering including some functionality to solve the 2D Schrödinger Eqn. :
H psi(x,y)=i hbar d/dt psi(x,y)
The first thing I'll try is for simple 2D potentials V(x,y), but it would be interesting to look at solving the 2 particle Schrödinger eqn. for V(x) and allowing the user to select the fermionic case for antisymmetric wavefunctions.
There are a lot of interesting things to learn about the many-body S.E. which simply can't be demonstrated from only looking at 1 dimensional examples. Even going to just the 2D case will greatly improve the educational value of the app, but of course- my real reason for doing this will be because I think it's cool and it's a chance to make some pretty graphics.
I've spent a few weeks messing around with some code and here's an example of the graphics I've come up with so far. (The final version will probably look completely different. This is a test!)
The pic shows the magnitude squared wavefunction |psi(x,y)|^2 for some arbitrary potential. The coloring is done according to the phase. I've also got a cut-off in which I'm not plotting any values |psi|^2<0.001.
In the app you'll be able to rotate and zoom into the wave function to view it from all different angles.
In case anyone is interested, some tech-details- The plotting is done with OpenGL which is quite a nice graphics programming language and it's simple enough that even I can learn it (or at least the rudiments). This is an orthographic display in which the viewing angle is represented internally by quaternions.
OK well, feel free to give me your opinions.
