Question

Question 4: (i) 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. [5 marks] (ii) Show that the density of states D as a function of energy є for free, non-relativistic. spinless particles of mass m, confined in two dimensions to an area A, is given by for ε 0. 2 marks] (iii) Using the result of part (ii), show that Bose-Einstein condensation does not occur for a 3 marks] two-dimensional gas of bosons.

Answer 1

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