What you see here, is the quantum mechanical simulation of 2 electrons in a wire, bouncing off each other, and halfly passing through a gap in the wire. My article about this is here.
Click on it to restart the simulation. It goes quite fast, so look intently!
To simulate more than one particle in quantum mechanics, one has to give the model more dimensions, so to simulate 2 dimensions in ordinary 3 dimensional space, one has to make a model with 6 dimensions, which is an awful lot, takes up far too much memory and computation in the computer, and is impossible to visualise.
To alleviate this, I simulate electrons in a wire, wich is just one dimensional, so the model gets to be 2 dimensional, which can be shown as pictures. The yellow cross is the single gap in the wire, reflecting electrons partly. The blue diagonal line is the symmetry of two electrons, meaning that electrons are identical, so the wave function shall not change amplitude when the electrons switch places.
The Schr÷dinger wave equation is shown on the left, with imaginary and real amplitude shown as green and purple. The probability of finding an electron in the wire, which is vertical, is shown in the middle column. The right image shows the joint probability of finding the 2 electrons.
The calculation method here is a fully explicit 6 point finite difference scheme, by me, with a little help from a friend. (Thank you Svein) It is fast, stable, and unitary.
Put here 2010.01.13 by Kim ěyhus (c)