The question itself is pretty self explanatory. I asked this to my chemistry teacher when he was doing the photoelectric effect while teaching atomic structure, and he just shrugged it off.
One possible mechanism that I thought up, is an atom with a unpaired electron (say hydrogen) to absorb one photon, and jump to a higher energy level, and then just immediately be hit by another photon with a different energy which raises it to an even higher level. Then finally the electron falls back into its proper non exited state releasing not two but only one photon which has the energy of both the initial photons, ideally combining photons.
Is this mechanism correct? Does it occur in nature? Do photons have other ways in which they merge? or do they not merge at all?
Best Answer
To answer the question in the title, yes, see this link. It is also possible to combine more photons in order to get superior harmonics. For this you have a list that you can use to get some fast info on Wikipedia on this link.
Now, related to the mechanism that you proposed, in principle it could work, but you have to take into account the selection rules, which allows only for some transition between the energy levels on a system, in your case the hydrogen atom. What this means, is the following. Say the hydrogen atom is on its ground state $0$. First photon changes this state $n$ and the second from state $n$ to state $m$. Now, if the transition from $m$ to $0$ is not allowed by the selection rules, then your mechanism won't work the way you intended. You might however get 2 photons with different energies from the initial ones.