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 &
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
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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