Today I am inquiring how one would calculate the particle separation probability density for 2 particles in a square well, for 2 distinguishable particles. We are given both particles wave functions as $\psi_1(x)$ and $\psi_2(x)$ with the probability separation density as $P(x_1-x_2)$. My biggest issue seems to be that I don't know how to create a wave function that is a difference between the two other wave functions.
My attempt at a solution
For a conventional wave function, we can calculate the spatial wave function probability density as:
$$P(x) = |\psi(x)|^2$$
Our problem wants us to calculate:
which I interpret as some function of both particles, $\Psi(x_1,x_2)$, not the difference of the two functions. How can we create such a function?