Question 2 (a) Write down the form of the Bose-Einstein Distribution and discuss the phenomenon of Bose- Einstein condensation for a boson gas in three dimensions. In particular, carefully explain why the chemical potential becomes very close to the energy of the lowest single-particle state at sufficiently low temperature and describe how that changes the usual approach of replacing a discrete sum over energies with a continuum integral. Discuss how the occupation of the lowest single-particle state changes as a function of temperature for temperatures below the Bose-Einstein condensation temperature. (b) Show that the density of states as a function of energy for free, spinless particles of mass m, confined in two dimensions to an area A, is given by D(E) Am 2 (c) Using the result of part (b), show that Bose-Einstein condensation does not occur for a two- dimensional gas of bosons.