Bosons in four dimensions Consider an ideal boson gas in four dimensions. The N particles in the…

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.

 

 

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