Why Does the Electron Jump Between Stationary States?

[Qubix]

I've been bothered by this question. Say we have an electron in it's ground state. According to quantum mechanics, that is a stationary state. Then we excite the atom and the electron jumps into a higher energy level. That is also a stationary state. The question is: Why does the electron jump back onto its initial state since both states are stationary?

 

[Meir Achuz]

The upper states are made unstable (and not completely stationary) by interaction with the EM field. This is treated in QED which goes beyod simple one particle QM.

 

[arunma]

On a related sidenote, I would really like to know why particles in non-relativistic QM emit photons when they make transitions between states. They never really explained that to me...even in QFT.

 

[alxm]

Excited states are only approximately stationary. The ground state is the only truly stationary state.

arunma, well this depends on what kind of level of detail that you want.
The most hand-waving would just be to point out that an electron is charged, a photon has an electrical field, and should thus be able to transfer energy to the electron, and so if the photon matches the energy and selection rules, you should be able to have a transition.

Somewhat less hand-waving, covered in most ordinary QM textbooks, is to treat your photon as a time-dependent oscillatory perturbation, do a little work, and out comes Fermi's Golden Rule as your transition probabilities, as a first order approximation. Now if you're talking spontaneous emissions, then your perturbation comes from a vacuum fluctuation/virtual photon, which is described by QED, and I'm pretty sure is covered in most QED textbooks.

The first thing you need to know when someone asks a 'why' questions is what level they want the answer to be on!

 

[arunma]

Excited states are only approximately stationary. The ground state is the only truly stationary state.

arunma, well this depends on what kind of level of detail that you want.
The most hand-waving would just be to point out that an electron is charged, a photon has an electrical field, and should thus be able to transfer energy to the electron, and so if the photon matches the energy and selection rules, you should be able to have a transition.

Somewhat less hand-waving, covered in most ordinary QM textbooks, is to treat your photon as a time-dependent oscillatory perturbation, do a little work, and out comes Fermi's Golden Rule as your transition probabilities, as a first order approximation. Now if you're talking spontaneous emissions, then your perturbation comes from a vacuum fluctuation/virtual photon, which is described by QED, and I'm pretty sure is covered in most QED textbooks.

The first thing you need to know when someone asks a 'why' questions is what level they want the answer to be on!

Hi alxm. I guess the "third year high energy grad student (who's taken QFT)" level of explanation is the one that I'd be most interested in.

However, the hand-wavy explanation is interesting too. Would I be right to say that a photon's electric field is basically adding an extra term to the electron's Hamiltonian, and thus causes the electron orbitals to no longer be eigenstates? If so, then is it possible to explain, within the confines of non-relativistic QM, why an electron will still return to its ground state even in a vacuum? Or are these transitions perhaps caused by the Coulomb potential only being an approximation to the atomic electron's Hamiltonian (since nuclei have a non-zero size)?

Thanks!

 

[ansgar]

if you want the explanation just pick up a QFT book and get your hands dirty.

the vacuum is not the vacuum of fields though, only vacuum of particle field excitations

 

[alxm]

Would I be right to say that a photon's electric field is basically adding an extra term to the electron's Hamiltonian, and thus causes the electron orbitals to no longer be eigenstates?

It's a perturbation, yes. It's true, though that if you have an excited state, then non-relativistically, it cannot decay if there's no interaction/perturbation/field coupling whatsoever going on.

But as I hinted at, you don't need a full relativistic description if you're only after a first-order approximation. But it's naturally more rigorous https://www.amazon.com/dp/0471293369/?tag=pfamazon01-20 covers it all in great detail.

 

[Qubix]

The first thing you need to know when someone asks a 'why' questions is what level they want the answer to be on!

I hear Richard Feynman talking :D

Anyway, thanks for the answers. It seems I have to go much further than Non-relativistic Quantum Mechanics to answer my question. I can't wait :)