(a) The grand partition function for a single particle state in a system of bosons is given by: Z = eBlu-e, jn, Discuss the constraint on the chemical potential u, and show that, provided that this constraint is satisfied, the mean occupation number of the single particle state in is given by: 1 ef(e,-)_1 (b) In the discussion of the physical properties and behaviour of He, we derived the equation: de -So R-4)_1' [7 marks] 2r(2m) /2 N= where N is the number of atoms in the system. Discuss the meaning and origin of each of the contributions to N in this equation