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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 x L × L x 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 dimen- sionless integral. 3. Below the Einstein temperature, calculate the occupation number of the lowest- energy, 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.

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 x L × L x 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 dimen- sionless integral. 3. Below the Einstein temperature, calculate the occupation number of the lowest- energy, 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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From the book: An Introduction to Statistical Mechanics and Thermodynamics
(Swendsen R.H.)

Problem 27.2 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 xL x L x 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 dimen- sionless integral. 3. Below the Einstein temperature, calculate the occupation number of the lowest- energy, 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.
Transcribed Image Text:Problem 27.2 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 xL x L x 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 dimen- sionless integral. 3. Below the Einstein temperature, calculate the occupation number of the lowest- energy, 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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