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Recently IBM created world’s smallest ever animation on an atomic scale video. Researchers made the animation using a scanning tunnelling microscope to move thousands of carbon monoxide molecules to show a boy dancing, throwing a ball and bouncing on a trampoline.

My question is, why in this video we see a pattern of dark and bright circles around each molecule? What do they represent?

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You are seeing the wave-like nature of matter. The atoms aren't completely isolated to a specific location and they exhibit wave properties. The rings around the atoms are the result of electron scattering off of the probability wave of the atom. The details of a scanning tunneling microscope (STM) may help.

The wave effect can be reinforced via constructive interference to create standing waves. See the ring in the upper right:

quantum corrals

These are quantum coralls and they can create a "quantum mirage" like the apparent atom at the center. The effect can be quite dramatic:

quantum corral standing wave

There isn't an atom in the center but the wave-nature of matter is quite obvious.

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Is it because the atoms themselves aren't localized to a specific location, or is it because their electron cloud exhibits wave properties? In the first case, I would expect that using atoms with heavier nucleus (at the same temperature) will reduce this effect. Moreover, aren't the CO molecules that have been used by IBM have enough momentum at this temperature so that their position could be regarded as a position of a classical object? –  Andrey B May 3 '13 at 22:14
    
@AndreyB I believe it's a combination of a few effects. The atoms definitely aren't completely localize and their electrons do exhibit wave-like properties. Further complicating the matter is the electric current the STEM used can itself setup an electron standing wave between the tip and an atom on the surface similar to the standing in the middle of the corral. –  Brandon Enright May 3 '13 at 22:33
    
I'm interested in the probability density $|\Psi(\mathbf{r}, t)|^2$ of finding an atom at a given position. Is it possible that the atoms are pretty well localized in space, and yet we will see those wave-like patterns in the STM image, e.g. a quantum mirage inside a quantum corall? –  Andrey B May 4 '13 at 19:09
    
@AndreyB that's a good question that you should ask on the site. It won't get noticed or answered properly as a comment. –  Brandon Enright May 4 '13 at 20:03

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