I'm confused why the quantum state of a photon is typically regarded as its momentum (which presumably is described by 4 numbers---wavelength, direction, and angular momentum) and not by its position (which seems to be described by 3 numbers).
I understand that position and momentum are complementary measurements, so as one is known more accurately, the other is known less accurately.
So perhaps this question should read, "what is the full quantum wave equation for a photon" ? Does this question even make sense? Or does it only make sense to describe photons as a transfer of energy from one atom to another atom?