I have read this question:
where Arnold Neumaier says:
photons do not have a spatial probability density
He specifically says that in the case a laser is shone on a surface, the beam does have a spatial probability density, for the surface where the beam hits it. That is understandable, but the double slit experiment is about single photons being shot one at a time, and they have to pass through slits, not shone directly on the screen.
Though, this paper talks about spatial probability density and photons.
Now the double slit experiment works well with both electrons and photons.
Though, electrons do have a spatial probability density.
To summarize, the probability distribution of the outcome is the normalized square of the norm of the superposition, over all paths from the point of origin to the final point, of waves propagating proportionally to the action along each path. The differences in the cumulative action along the different paths (and thus the relative phases of the contributions) produces the interference pattern observed by the double-slit experiment.
As I understand the main difference is that photons do not have a position operator.
where Chiral Anomaly says:
Saying that a photon doesn't have a wavefunction can be misleading. A more accurate way to say it is that a photon doesn't have a strict position observable.
where Punk_Physicist says:
There's an old argument by Newton and Wigner, that the photon as a massless particle can't have a position operator and therefore no position space wave function. The interference you see in a double slit experiment is due to interference of the field mode itself
Without strict photon position observable (spatial probability density), how is the double slit experiment possible?