Can one derive the photon number / phase uncertainty relation

[snoopies622]

In an earlier thread of mine, another physics forums member was nice enough to point out that there is an uncertainty relation between photon number and wave phase for light.
https://www.physicsforums.com/threads/is-there-a-frequency-eigenstate-for-light.727141/
Now I am wondering, where does this uncertainty relation come from? Was it discovered experimentally or can it be derived from other quantum mechanics axioms?
I am guessing that the answer lies in analysis of the quantum harmonic oscillator, but I am not sure.

 

[blue_leaf77]

See the first section in http://hitoshi.berkeley.edu/221a/coherentstate.pdf

 

[snoopies622]

Thanks, blue Leaf77!