I am learning identical particles recently, but I have some problem interpreting what I am writing down. So if we have two distinguishable particles, absolute value of ψ(x_1, x_2) tells the prob. density of finding the first particle at x_1 and the second at x_2. But for identical particles, it seems to me that it doesn't make sense to--and we can't-- label the particles with numbers. So what is the proper interpretation of the absolute value of ψ(x_1, x_2) in this case? (I guess I understand how the stuff on interchanging the particles works, but just can't wrap my head around the above interpretation) Also, for identical particles, how do I calculate the probability density of "finding A particle in x_1 and A particle at x_2"? I mean, classically, it would be the sum of "finding the first at x_1 and the second at x_2" and "finding the first at x_2 and the second at x_1", but this can not be the way it works in QM, right? Thank you so much.