Two Dimensional Well Exercise #3

Please answer the  following 2 questions regarding the Physlet:

Description

Shown is the wave function for two non-interacting and identical (or indistinguishable) particles in a one-dimensional infinite square well (We can call them particles "1" and "2").  One dimension (x) represents one particle  and the other side (y) represents the other particle. You may click-drag around the axes and use a shift-click-drag to zoom.

Questions

1. Given a wave function that looks like: y(x₂, x₁) = y₁(x₂)y₂(x₁), what do the ones and twos (the subscripts) mean?
2. Which probability density represented above represents a symmetric state and which one an anti-symmetric state.

Credits

Script by Mario Belloni.
Questions by Mario Belloni.
Java applets by Wolfgang Christian.