A single photon can have any wave function. In general, it would not be just a single plane wave with a fixed momentum. A general wave function can be expressed as a spectrum of plane waves (also called an angular spectrum). The expectation value for the momentum of the photon is then given by a simple calculation involving the spectrum. When you transform the spectrum to the spatial domain you'll get the probability amplitude, from which you can get the detection probability for the photon at a specific location.

A single photon can have any wave function. In general, it would not be just a single plane wave with a fixed momentum. A general wave function can be expressed as a spectrum of plane waves (also called an angular spectrum). The expectation value for the momentum of the photon is then given by a simple calculation involving the spectrum. When you transform the spectrum to the spatial domain you'll get the probability amplitude, from which you can get the detection probability for the photon at a specific location (integrated over the area of the detector).