Two particle probability density

[daudaudaudau]

If I have a wave function $\Psi(x,x')$ for two identical fermions, then I have learned that the particle density at $x$ is
$$n(x)=2\int|\Psi(x,x')|^2dx'$$

$|\Psi(x,x')|^2$ is the probability density of finding a particle at $x$ and a particle at $x'$. Does this mean that $\int|\Psi(x,x')|^2dx'$ is the probability density of finding a particle at $x$ ?

 

[alxm]

Yes, the particle density and probability density are the same thing.