Oscillating System Composed of Two Hydrogen Atoms

[sparkle_pony]

Assume a system of two hydrogen atoms. No other matter exists inside or outside of the system. Initial condition is one H with an electron in the n=2 state. That state decays to ground and emits EM that is absorbed by the electron on the second H. Repeat forever (maybe).

Some questions:
Is the "space" occupied by these atoms effectively 1-D with each atom being the end points. I.e. the EM couldn't be emitted outside of those bounds.
Would the oscillation continue forever or would it decay somehow?
Since there is no reference matter to compare to would it the size of each atom and their distance from each other be undefined?
Since the above is undefined then so is the frequency of oscillation?

This is not a HW problem. I'm posting this to get a better understanding of the matter/space connection. I wish there was a forum entitled "dumb speculative questions".

 

[.Scott]

When the photon is emitted, why does it head in the direction of the other atom?
Are supposing a (2-atom) hydrogen molecule.

 

[sparkle_pony]

That is the heart of one of my questions. Would the wave vector be in any direction other than the other hydrogen, since no other matter exists in this system?

 

[dauto]

1st The photon can be emitted in any direction.

2nd the distance between the atoms can still be defined.

 

[.Scott]

1st The photon can be emitted in any direction.

Sparkle Pony may have a point here. If the photon heads off in the "wrong" direction, there will be nothing to collide with so it can never complete its journey. In QM, a journey never completed is a journey never created.
Something different would happen. I'll let others who are more acquainted with QM describe what.

 

[Khashishi]

I think infinity is usually treated as some kind of giant absorber. But if space is finite (like the balloon model), what would happen? I don't think we understand the boundary conditions of the universe well enough to answer this question definitively.

Let's start with a simpler system. One atom, spherical space. By symmetry, the wavefunction should be symmetric around the atom. I don't think a photon can be emitted in any particular direction, unless there is something else in the universe to detect it, since an observation is required to collapse the wavefunction and break the symmetry.

With two atoms, I guess you would have a axially symmetric system. The ground state would have some energy equally spread among both atoms. But if the atoms were far apart, just a little nudge could send it into some superposition state that is oscillating the energy between both atoms. This could be interpreted as a photon traveling between the atoms. But photons and individual atoms are really an idealization.

 

[dauto]

I think infinity is usually treated as some kind of giant absorber. But if space is finite (like the balloon model), what would happen? I don't think we understand the boundary conditions of the universe well enough to answer this question definitively.

Let's start with a simpler system. One atom, spherical space. By symmetry, the wavefunction should be symmetric around the atom. I don't think a photon can be emitted in any particular direction, unless there is something else in the universe to detect it, since an observation is required to collapse the wavefunction and break the symmetry.

With two atoms, I guess you would have a axially symmetric system. The ground state would have some energy equally spread among both atoms. But if the atoms were far apart, just a little nudge could send it into some superposition state that is oscillating the energy between both atoms. This could be interpreted as a photon traveling between the atoms. But photons and individual atoms are really an idealization.

That's not correct. Symmetry can be spontaneously broken. The rest of the universe's got nothing to do with the emission that happens locally and spontaneously. A hydrogen atom in a excited spherical state (say 2s) will decay by a photon emission. The photon will leave in some random direction and the final state (atom + emitted photon) will not be spherically symmetric. Nothing wrong with that. That's how Quantum Mechanics works.

 

[.Scott]

That's not correct. Symmetry can be spontaneously broken. The rest of the universe's got nothing to do with the emission that happens locally and spontaneously. A hydrogen atom in a excited spherical state (say 2s) will decay by a photon emission. The photon will leave in some random direction and the final state (atom + emitted photon) will not be spherically symmetric. Nothing wrong with that. That's how Quantum Mechanics works.

The OP said "no other matter exists inside or outside the system". This means that when the photon is emitted in a random direction - not reaching the other hydrogen atom, that event happens in near total isolation. If we assume that the hydrogen atoms are not at escape velocity relative to each other, even after the photon emission, then they will orbit each other. If that orbit occurs, then the missing photon will become evident to the other hydrogen atom - a sort of minimal measurement.

What I think really happens, and someone can confirm this, is that the different combinations of emissions and orbits will become a superimposed quantum state that will never be resolved because there's not enough stuff in that universe to collapse the state.

 

[Khashishi]

That's not correct. Symmetry can be spontaneously broken.

You sure about that? It depends on what exactly provokes a collapse of the wavefunction. With nothing else in the universe, there is no quantum decoherence, and everything should evolve nice and smoothly.