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From reading many questions on this site I have the following conclusions:

  1. Interaction of a photon and a free electron is an instantaneous process of scattering (transfer of momentum) between said particles.
  2. Interaction of a photon and an electron bound in atom is a very fast but not instantaneous (electron cloud has to restructure itself via resonant oscillation) process of absorption in which the photon is annihilated and atom ends up in excited state. Later another photon can be emitted from the atom taking away the excitation. This is not scattering as scattering happens for free electrons and absorption for bound.
  3. Virtual photons (and other virtual particles) don't exist and are only a mathematical tool. Any view that they are "real virtual photons" is wrong.

Now to the questions:

  1. I was told that spontaneous emissions is a stimulated emission, stimulated by a vacuum fluctuation photon coming from $ \frac{\hbar\omega}{2}$ in the photon field hamiltonian. How do I connect this with the fact that virtual photons don't exist?

  2. In a process of second harmonic generation, are photons absorbed or scattered, as there is no real absorption? Is "virtual energy level" also only a mathematical tool? If so, why SHG is stronger if there is a real energy level nearby? How would SHG look on a Feynman diagram? How would it look on a Bloch sphere?

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