In Yanhua Shih's book on quantum optics, the coherence functions are expressed in terms of effective wave function. Here are the expressions for single photon wave packets.
To derive the coherence functions we have used Heisenberg picture where the field operators, not the wave functions, are time dependent.
We can also take a look at the effective wave function for thermal source.
So, it is confusing why we have a wave function with time as a parameter. What is the physical significance of effective wave function?