# What do you see in 'A Boy and His Atom'

A boy and his atom is a short movie by IBM animated by actually moving atoms around and using a scanning tunneling microscope to display the result. When I first saw this picture I was fascinated because you can actually see a real world example of quantum mechanics which is otherwise so abstract. You can see the standing waves formed by the electron clouds. But this makes me wonder what exactly do we see.

Here's what I understand from STM's: an STM works by probing some surface with a conductive, sharp tip. If the tip gets close enough to the surface the voltage difference causes electrons to tunnel to the tip which induces a current in the probe. For each pixel the tip is moved through a range of distances to get current as a function of distance to the surface.

My first question is what is the waviness we see? Is it the eigenstate of the electrons in the metal? Is it the ground state? Is this a static wavefunction or is the picture time-averaged?

My second question is how is the current measured? Does the current consist of a single electron and is the current proportional to a probability current: $$j=\frac{\hbar}{2mi}(\Psi^*\nabla\Psi-\Psi\nabla^*\Psi)$$ or does the current consist of multiple electrons? Do the electrons that tunnel get replaced by other electrons from the metal?

That were a lot of questions so any answers are appreciated.

The currents are lots of electrons, for example $$1$$ nA = $$10^{10}$$ electrons per second.