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I saw the answer sometimes ago in a book "Quantum Electronics" or similar title. I don't remember the author since I lost the book. The book sets ( I believe so ) a constant electric current $I$ in a cable along the $z$ axis. Then, after a long ( but not straightforward ) calculation it arrives to the result I mentioned above.

Edit: A possible analogous calculation that OP refered to, Klein-Gordon particles generated by a classical source: problem 4.1 in these notes(In fact a solution manual to Peskin and Schroeder). If this is not what OP refered to, please delete it.

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  • $\begingroup$ There is a not so clear discussion in "Fundamentals of Quantum Optics, J. R. Klauder and E. C. G. Sudarshan, Section ${\bf\mbox{7-4 B}}$, pag. 141. W. A. BENJAMIN, INC 1968". $\endgroup$ – Felix Marin Nov 5 '13 at 6:48
  • $\begingroup$ +1, I've only seen a perturbative calculation finally giving a poisson distribution, I'd like to see if there is a more insightful approach. $\endgroup$ – Jia Yiyang Nov 5 '13 at 7:08
  • $\begingroup$ what sort of a device gives the photons? a dc current incandescent lamp? Is this connected with Shot noise? $\endgroup$ – anna v Nov 5 '13 at 7:58
  • $\begingroup$ @JiaYiyang Thanks. Your addenda is quite right and it adds more insight into my question. $\endgroup$ – Felix Marin Sep 2 '14 at 23:01

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