# Oscillating System Composed of Two Hydrogen Atoms

• sparkle_pony
In summary: However, I do remember reading about a quantum vacuum catastrophe, where the zero-point energy in an otherwise empty universe would be infinite. So maybe that's related?In summary, assuming a system of two hydrogen atoms with no other matter present, the initial condition is one hydrogen atom with an electron in the n=2 state. The state decays to ground and emits EM that is absorbed by the electron on the second hydrogen atom. This process repeats indefinitely. Some questions arise, such as whether the "space" occupied by these atoms is effectively 1-D and if the oscillation would continue forever or decay. Without any reference matter, the size of each atom and their distance from each other is undefined, making the frequency of oscillation also undefined
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".

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

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?

1st The photon can be emitted in any direction.

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

dauto said:
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.

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.

Khashishi said:
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.

dauto said:
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.

dauto said:
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.

## What is an oscillating system composed of two hydrogen atoms?

An oscillating system composed of two hydrogen atoms is a physical system in which two hydrogen atoms are connected by a force that causes them to move back and forth in a periodic manner.

## What is the significance of studying oscillating systems composed of two hydrogen atoms?

Studying oscillating systems composed of two hydrogen atoms can provide insights into the behavior of molecules and chemical reactions. It can also help in understanding the fundamental properties of atoms and the forces that govern their interactions.

## What factors affect the oscillations of a system composed of two hydrogen atoms?

The oscillations of a system composed of two hydrogen atoms can be affected by various factors such as the distance between the atoms, the strength of the force that connects them, and the initial conditions of the system.

## What are the different types of oscillations that can occur in a system composed of two hydrogen atoms?

The most common types of oscillations in a system composed of two hydrogen atoms are harmonic oscillations, where the atoms move back and forth with a constant period, and anharmonic oscillations, where the period changes over time due to the non-linear nature of the forces between the atoms.

## How can oscillating systems composed of two hydrogen atoms be modeled and studied?

Oscillating systems composed of two hydrogen atoms can be modeled and studied using mathematical equations and computer simulations. These models can help in predicting the behavior of the system and understanding the underlying physical principles.

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