Problem 4 - Non-interacting Boson Gases in 2D Consider a non-interacting gas of N spinless Bosons confined to two dimension (e.g. on a surface) of area L2. We want to calculate if Bose-Einstein Condensation is possible for both massive and massless Bosons in 2D. First consider Bosons with mass, such that the allowed quantum energies are given by Eni 2mL2 n , = nx t ny, nx, Ny = 1, 2, 3, . . . (a) (2 points) Show that the density of states for a spinless Boson with mass in 2D is mL? D(E) = (b) (3 points) Following the derivation in K2 and the notes for 3D, write the integral expression for the total number of particles in all excited states Nex in 2D. Comparing your expression with the 3D one, discuss why Bose-Einstein Condensation (i.e. where Ner