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- TL;DR Summary
- Any linear combination of atom's states is possible, so atom should be able to absorb any amount of energy. Though, as we all know, it doesn't. Why?

Let's say atom has two energy levels, ##E_1## and ##E_2##. If atom is in the first state ##|E_1\rangle##, then it's able to absorb a photon with energy ##E_2-E_1##, while transitioning to the second state ##|E_2\rangle##. In atom's spectrum we can see an absorption line at the corresponding frequency. So far so good.

But atom doesn't need to be in energy eigenstates, does it? So one can imaging atom transitioning from ##|E_1\rangle## to e.g. ##\frac{1}{\sqrt 2}(|E_1\rangle + |E_2\rangle)##. Energy, required for the transition, is ##\frac{1}{2}(E_2-E_1)##, why don't we see an absorption line at the corresponding frequency?

But atom doesn't need to be in energy eigenstates, does it? So one can imaging atom transitioning from ##|E_1\rangle## to e.g. ##\frac{1}{\sqrt 2}(|E_1\rangle + |E_2\rangle)##. Energy, required for the transition, is ##\frac{1}{2}(E_2-E_1)##, why don't we see an absorption line at the corresponding frequency?