Thursday, February 16, 2012

Simulation of quantum wave function

Had a lecture in quantum mechanics today, we've been starting to get serious and are now working with arbitrary 1 dimentional potentials. While doing the work I feelt desperatly in need of some visualization. Therefore I packed together a little simulation in haskell this afternoon. Now, Haskell is the right tool for this kind of job. The whole program is just 63 lines of code, and they're ugly too. I bet that it could be crammed down if one wanted. Anyways, Haskell is so great at this stuff for many reasons. For example it lets me define Numerical instances of functions, that mean that i can add two functions together, before I give them the arguments. This is great for building up complex mathematical functions. In the future I'd like to extend this example to generate a wavefunction for an arbitrary potential. This requires solving differential equations though, I don't think Haskell's typesystem is up for that yet. Anyway I'd be interested in ways to express maths, especially differential equations in Haskell, if you have any ideas, tell me!

The code, as always is available at github

The video represent the wave function of a quantum particle in a box. Unlike normal things in day to day life, quantum partilces doesn't have a defined possition, they have a probability of being at given possitions. The y axis of this animation represents the probability of finding the particle at a given point. This specific example is the superpossition of the 4 first exited states of a box particle. As you see, the "possition" that is where you would expect to find the particle changes with time. That mean we have a moving particle. That might not sound strange, but if i say that each of the 4 exited states in themselves are stationary, they don't move at all, then things start to become interesting. The thing is that by superpositioning differnt static states, you can create a new state, that is dynamic, and thus move; exciting!

The video is generated from a series of pictures output by my haskell program. Since I don't know of any good way to create interactive plots in haskell, and this was an 2-hour evening project i decided to go for: Loads of images -> ffmpeg -> video -> profit!

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