Quantum interpretation of light coherence

That's a very good question, but is actually very difficult to answer. The problem is that to understand the quantum mechanics of light, you really have to understand quantum field theory, not just quantum mechanics. Quantum field theory is necessary to reconcile relativity (as light is inherently relativistic) and quantum mechanics.

If you look around the literature, you won't really see anybody writing out the wave-functions of a single photon. People will write wave functions of electrons when they are moving much slower than the speed of light (as they are able to move slowly because they have a mass), but never of photons. The reason for this is that, in quantum field theory, you really have to think about all the photons at once, not just one photon at a time.

When an atom emits a lone photon, there is no conception of whether that photon is "coherent" or not. Coherence is a property that many photons share with each other. Usually, when light is emitted, like in a light bulb or from the sun, the light is not coherent. To get single color coherent light, as described by Maxwell's laws before people knew about quantum mechanics, you perversely need to use a quantum mechanical mechanism, namely a laser. I do not really understand how a laser works, but somehow it exploits multiple energy levels in an atom to release light that is coherent with all the other light around it.

The quantum field states that most closely resemble classical waves are called "coherent states." Coherent states are states of the quantum photon field, for example, that are as close to the classical electro magnetic waves as is allowed by a generalized notion of Heisenberg's uncertainty principle. These are the states that a laser produces.

So it's weird: photons are quantum mechanical, but a laser can produce them coherently in a way that mimics classical mechanics.