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Usually photons are considered to have the possibilty to behave as a quantum. The quantization in an atom is because of the nature of the Coulomb force coupling the electron to the nucleus.

But why can't the photon transfer part of its energy to the electron (enough to transition between two energy levels) and then travel on with reduced energy? After all, it can transfer enough energy to completely ionize the electron ( Compton scattering) so why not just enough to excite the electron between two energy states?

Marijn
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    That is not what Compton scattering is. –  Dec 12 '16 at 22:07
  • Have a look at a similar question and answer of mine http://physics.stackexchange.com/questions/216040/can-an-electron-jump-to-a-higher-energy-level-if-the-energy-is-insufficient-or-e/296138#296138 and links therein – anna v Dec 15 '16 at 20:09

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What you are describing is inelastic scattering. An example of this is Raman scattering. This is used in Raman spectroscopy to study low-lying excitations using light that has higher photon energy. Also in Compton scattering there is a scattered photon with lower energy.

(And these processes also happen the other way around. The Raman spectrum has anti-Stokes lines at higher photon energy. Or one can scatter a high-energy electron off a laser photon to produce a gamma.)

  • But is Raman scattering also about electrons getting a higer energy state or only about molecular vibrations? – Marijn Dec 13 '16 at 10:10
  • @Marijn Also for electronic transitions and magnetic excitations. I have been working in x-ray Raman scattering. It is a field that now has some new instruments with very high resolution, and capabilities similar to inelastic neutron scattering because of the x-ray momentum. –  Dec 13 '16 at 10:33