What you see, are the states where the particles are close to each other, becoming more probable as time goes by, without the particles being localized anywhere, except near to each other. Wave function to the left, and probability to the right.
Click on it to restart the simulation. It takes a while, so be patient!
This is a quantum mechanics simulation of 2 electrons in a wire, randomly distributed, bouncing off each other, and halfly passing through a gap in the wire. Two electrons in a one dimensional wire, must have a two dimensional simulation.
I quite serendipitously discovered this crystallization effect when rewriting the code. There is no radiation involved to get at these lower states, just randomness evolving in time with the particles attracting each other, and halfly reflecting through the gap in the wire, changing phase about 90 degrees there.
This might be akin to cooper pairing; the leading theory of superconductivity.
It is also somewhat like quantum collapse, according to the K°benhavn/Copenhagen interpretation, in the sense that the probability distribution collapses into a tighter space. I did not think this was possible, because the math is linear and unitary, but the probability is not, which might be the explanation. My article explaining the Many-Worlds interpretation mentions this in bullet points No 3, but this shows that this point might be wrong. It has perhaps some bearing on the Born probabilities as well. I do not know yet. I have to ponder some on this, when I get the time and inspiration.
Put here 2010.01.17 by Kim ěyhus (c)