Bosons in four dimensions
Consider an ideal boson gas in four dimensions. The N particles in the gas each have mass m and are confined to a box of dimensions L × L × L × L.
1. Calculate the density of states for the four-dimensional, ideal Bose gas.
2. Calculate the Einstein temperature in four dimensions in terms of the given parameters and a dimensionless integral. You do not have to evaluate the dimensionless integral.
3. Below the Einstein temperature, calculate the occupation number of the lowestenergy, single-particle state as a function of temperture, in terms of the Einstein temperature and the total number of particles.
4. Calculate the chemical potential below the Einstein temperature.