Elektromagnetic field ~ probability amplitudes

[birulami]

Given an electromagnetic field by its components E and B. How is this related to probability amplitudes of a Schrödinger wave function for the same field.

Trying the same or at least a similar question from a different angle: given the E and B field, can we derive from it, in principle, not considering solvability, the probability of registering a photon within a certain (small) volume and time interval?

If not, which piece of information is missing. Yet another angle on the question: do the E and B field contain all the information for the probabilities or is there something missing?

 

[vanhees71]

The electromagnetic field is a relativistic massless spin-1-field. There is no physically sensible interpretation of it as a single-particle wave function as for massive particles in non-relativistic (Schrödinger) quantum mechanics. There is not even a proper position operator for photons!