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Say you have some material with enough bandgap for a photon to be absorbed by an electron. The electron goes to a higher energy state. What happens after that?

I would expect the electron to go back to a lower energy state and release a photon. Does it release only one photon? Does it have the same energy, i.e. can it release two photons whose energies add up to the original photon? Does it scatter? In the classical case we would expect to have reflection/refraction. What happens in the quantum case.

Also, now that there is a free electron state available, can a second electron fall to it and release a low energy photon etc.? Or does the highest energy electron try to fill that state?

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One has to keep clearly in mind that a bound state, like an atom or a molecule or a crystal lattice, involves more than electrons. There are protons in the nuclei of atoms generating the potential well which we usually assume that the electron is trapped in. It is a convention, due to the fact that the mass of the electron (~0.5 Mev) is so much smaller than the mass of the proton ( ~0.938 MeV ) that even for the simple hydrogen atom, it is usual to talk of electron energy levels. The large mass of the nucleus makes the assumption reasonable, that the center of mass of the problem is on the positive charges and it is the electrons that are moving in orbitals. The energy levels characterize the atom as a whole , they are the fingerprint of the atom, not the electrons or the nuclei individually. With this in mind

I would expect the electron to go back to a lower energy state and release a photon.

That is what happens, the excited atom deexcites with the emission of a photon.

Does it release only one photon?

If there exists empty energy levels below the excited energy level, then the energy could be released in a cascade of photons.

Does it have the same energy, i.e. can it release two photons whose energies add up to the original photon?

These will add up to the energy of the original photon .

Does it scatter? In the classical case we would expect to have reflection/refraction. What happens in the quantum case.

No, it does not scatter within the time constants of the interaction. Once a photon is emitted, then of course it can scatter on other atoms.

Also, now that there is a free electron state available, can a second electron fall to it and release a low energy photon etc.?

There are many "free" energy levels over the neutral filled levels for all atoms.

An electron may be caught in an energy level above the neutral atom's level, creating a negative ion, depending on the filled energy levels of the atom.

Or does the highest energy electron try to fill that state?

No, it is energy levels one is talking in quantum mechanics, of the bound state. The electrons and the nucleus are not independent agents.

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  • $\begingroup$ I don't quite understand your last paragraph. I mean that an electron absorbs the photon and moves to a higher energy level. Now there is space available for an electron where the original one was i.e. the wave function of the electron before it absorbed the photon is allowed(Pauli's exclusion principle). Also, the system is trying to minimize the energy i.e. fill the energy bottom up. Is this available space going to be filled with the electron that has the highest energy? I'm also thinking here from the perspective of semiconductor physics, where all the electrons are treated together. $\endgroup$ – user110971 Sep 23 '16 at 20:13
  • $\begingroup$ You are not thinking in quantum mechanical terms, which really are the WHOLE atom/molecule/latice. The whole atom will be described by a new wavefunction, one that has a hole in the lower energy level. An electron from a higher energy level will fill the hole, and a photon will leave the atom with the energy of transition. If the hole is in the middle of the electron shells, a cascade is probable. So it might be the highest level that empties, or it might be emptied after another level below it becomes available by the cascade. It is all probabilities that have to be estimated for each case $\endgroup$ – anna v Sep 24 '16 at 4:02
  • $\begingroup$ see en.wikipedia.org/wiki/Electron_configuration $\endgroup$ – anna v Sep 24 '16 at 4:03
  • $\begingroup$ yes, I am familiar with orbitals etc. I should clarify that I have an engineering background. We have always treated the electrons separate from the atoms. After all, they are the charge carriers. Is this wrong? Can you not treat the electrons as having their own wave functions? You can always add up all the wave functions to get the wave function of the system. What about free electrons that are not bound to any atoms? From the perspective of the bandgap energy don't you treat all electrons together? I'm thinking here about Bloch's theorem and the Fermi-Dirac distribution. $\endgroup$ – user110971 Sep 24 '16 at 10:49
  • $\begingroup$ The nuclei are also charge carriers, the electrons are more mobile in certain lattices, and model can be devised which approximate the complete solution of the lattice, all many body problems are solved with various approximations even classically. You cannot add up wavefunction except in specific boundary conditions : adding up photon wavefunctions gives the classical elemctromagnetic wave. Wavefunctions are solutions with specific potentials and boundary conditions. A free electron fulfills the Dirac equation with a zero potential. A blloch wavefunction has a periodic potential $\endgroup$ – anna v Sep 24 '16 at 11:09

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