Observer vs Natural phenomenon

[jaydnul]

If you have two hydrogen atoms as your system, then you use the many body Schrödinger equation for 2 protons and 2 electrons. The coulombic repulsion between the two atoms is built into the SWE, so is there a range of different possible magnitudes for the repulsion? If so, does the system decide at which magnitude to repel based on quantum randomness? Lastly, how would that translate to the macroscopic world. Is the range of different possibilities just too small to ever notice?

The reason i ask this is because when i, say, push on a chair, my finger atoms and the chair atoms are definitely repelling, so is that system just randomly choosing the magnitude of repulsion?

 

[Nugatory]

The reason i ask this is because when i, say, push on a chair, my finger atoms and the chair atoms are definitely repelling, so is that system just randomly choosing the magnitude of repulsion?

No, it's averaging across an enormous number of individual atoms and (as expected) ending up with something very close to the expectation value.

For a classical analogy, you could consider the tabletop in front of me (supports my bare feet and because it's too early in the day for cold beer, a nice warm cup of coffee). It is being bombarded by randomly moving air molecules on both sides, yet it experiences no net force because on average the number and speed of the molecules hitting the top are balanced by the number and speed of the molecules hitting the bottom. It is in principle possible for every one of the $10^{24}$ or so molecules underneath the table to randomly happen to be moving up at the same time; if this were to happen the table would blast through the ceiling like an artillery shell. And the probability of this happening? It's on the order of $2^{-(10^{24})}$, a number which is indescribably small.

 

[jaydnul]

No, it's averaging across an enormous number of individual atoms and (as expected) ending up with something very close to the expectation value

But what about a system with just two hydrogen atoms colliding without any other potentials, a completely isolated area. I realize that wouldn't happen, but just as a thought experiment. Would that system randomly choose an eigenvalue for repulsion?