Transitions between states in the atom are in discrete energy levels, as shown by Schrodinger's Equation. In order to go to a higher state, the atom must adsorb a photon of the exact energy as the gap between states. I wonder if such a photon exists.
I think a good analogy (which is probably the source of my error) is our representation of a number. There are infinitely many numbers between 1.01 and 1.001 which means that we would need infinitely many photons to have a continuous range of photon energies so that one would be the discrete, exact, energy.
A simple counter argument would be that we witness these transitions all the time - but the transitions we see the source atom is in external fields, and these fields result in splitting of the bands.
I think somewhere I am making a grave mistake, so if you find it please let me know.
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