We treated Bose-Einstein condensation in class for gas particles in a three-dimensional box.
Here, we consider a gas of bosons in a two-dimensional box.
(a) (4 points) Derive an expression for the density of states in terms of the energy, $g(\epsilon)d\epsilon$.
Follow the same method we used in class, but for a 2D space.
(b) (2 points) Try to set the chemical potential $\mu = 0$ in the integral over the density of
states giving the total number of particles $N$,
$N = \int_0^\infty d\epsilon \frac{g(\epsilon)}{e^{\beta(\epsilon-\mu)} - 1}$.
(3)
Can you get a finite $N$ at finite nonzero $T$? So, is it possible to have Bose-Einstein
condensation in 2D?
