I.e., can two photons completely overlap and propagate in the same direction?
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4Possible duplicate of Why do two beams of light pass through one another without interacting? – Yashas Apr 09 '17 at 03:13
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Related: Do photons interact with each other or with themselves only – Yashas Apr 09 '17 at 03:14
3 Answers
Photons are bosons. As such they obey Bose-Einstein statistics. One of the results of this is that bosons actually like to be in the same state. This is the reason for Bose-Einstein condenstates. It also the reason behind stimulate emission.
So, yes indeed, two photons can completely overlap and propagate in the same direction, or in other words, exist in exactly the same state.

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Yes. A 'classical' wave is a wave composed of a large number of completely coherent photons.

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Photons are point particles in the standard model of particle physics and as such they are described by a wave function which is a solution of a quantized Maxwell's equation.
Wave functions can be superimposed in space time, with no problem. It is the complex conjugate squared of the wave function which gives the probability of finding a photon at an (x,y,z,t). (Superposition gives the diffraction patterns observed in laser beams , and it is not an interaction).
If there is a possible interaction vertex, then some of the photons would interact and change direction, but the probability is very very small as there are four electromagnetic vertices in the feynman diagram.

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