Find the different eigenfunctions of a system of two particles (i = 1 or 2) that can be formed from the four single-particle eigenfunctions, ψ1(i), ψ2(i), ψ3(i), and ψ4(i).

Each eigenfunctions correspond to a different two-particle state.

(a) If the particles are distinguishable (i.e., not identical), one possible eigenfunction is ψ1(1)ψ2(2). Using this abbreviated notation, write down the correspond- ing eigenfunctions of the 16 different two-particle states.

(b) If the particles are identical fermions, one (un-normalized) two-particle eigenfunction is ψ1(1)ψ2(2) - ψ1(2)ψ2(1). How many different two-particle states are there? What are the corresponding (un-normalized) eigenfunctions?