When do we see particles to be in a superposition of energy states? I have two doubts:
Exactly when does this happen?
and
If we are in a superposition of states (lets say E1 and E2) and the particle absorbs a photon, what will happen? If E3-E1 = hf, will it go to E3?
Thanks!
 A: 
When do we see particles to be in a superposition of energy states?

From the fundamentals of quantum mechanics for "seeing" , i.e. measuring an energy, the result will be one unique energy eigen value "to every observable there corresponds an operator which acting on the state function will return an eigenvalue". So for an individual particle the answer is "never". For an ensemble of particles one could have some at an E1 level and some at the E2 level  and photons with energy E1 could kick out an electron when scattering off an E1 level particle and the E2 from the E2 level particle. Otherwise the photon will go through without interacting. ( transparency ).
One can infer that a single particle is in a superposition of energy levels if one measures a variable that does not commute with energy, by construction of quantum mechanical states. We trust the mathematics because there has not been a falsification of quantum mechanical predictions to date.
Ensembles of particles can be prepared and are prepared in a superposition of states that allow accurate measurements  of energy levels, by using photon beams of two frequencies. Here is an example.
A: To see the particle in the superposition of state(say state 1 and state 2), you need to prepare many identical systems; the collection of many identical systems is called an ensemble. Then you need to measure the energy of each system, you will find sometimes you will get E1 and sometimes you will get E2, thus you can confirm yourself that the particle is indeed in the superposition of E1 and E2.
About what happens we you let a photon to interact with the particle, I think the photon will first to make the particle to collapse to one of its eigenstate(this process actually is a measurement). If the particle collapse to E2, nothing happens afterwards; else, it will jump to E3.
