Can Classical Mechanics and/or Quantum Mechanics explain the formation of a single hydrogen atom?

Question

If we have a single electron and a single proton, Can Classical Mechanics and/or Quantum Mechanics explain why the electron revolves around the proton and not the proton around to electron?

Answer 1

Classical mechanics does just fine with this.

1. Newton's Third Law says that the magnitude of the force exerted by the proton on the electron is equal to the magnitude of the force of the electron on the proton.

2. Newton's Second Law says that if the same force is exerted on two objects of unequal masses, the less massive object will accelerate more. What's more, its acceleration will be inversely proportional to its mass.

3. Experimentally, the electron is found to have much less mass than the proton.

4. Thus, the electron will accelerate much more than the proton when they interact.

Note that this doesn't prove that the proton is fixed in space. In fact, in a "classical atom" both the proton and the electron will each move in a circle around their common barycenter instead (aka their center of mass). But the barycenter is much much closer to the proton than the electron, and so its circular path is sufficiently small that we can get away with treating it as fixed to a good approximation.

Quantum mechanically, the picture is much the same: instead of using the position of the electron and the proton to describe our system, we use their center of mass and their separation vector instead. Because of the large mass ratio between the proton and the electron, the center of mass location is almost (but not quite) equal to the proton's location, and the separation vector then gives the displacement between the proton and the electron.