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A gas of N spinless Bosons of mass m is enclosed in a volume V at a temperature T. a) Find an expression for the density of single-particle states D (E) as a function of the single-particles energy E. Sketch the result. b) Write down an expression for the mean occupation number NE f a single particle state as a function of & , ,and the chemical potential (T). Draw the function on your sketch in part (a) for a moderately high temperature, that is, a temperature above the Bose-Einstein transition. Indicate the place on the €-axis where € =p. c) Write down an integral expression that implicitly determines u(T) . Referring to the sketch in (a) determine in which direction (T) moves as T is lowered. d) What is the (T) for T < Tc ? Describe NE (E,T) for T < Tc. .

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