This is standard text book stuff, but I found it useful to collect the key formulae and results into a few pages. The Fermi-Dirac and Bose-Einstein distributions are just stated rather than derived. However, the formulae for the temperature of a Bose-Einstein condensate is derived in detail from the underlying distribution. Similarly, the Fermi energy defining a degenerate fermion gas is derived in detail. It is pointed out that the two expressions are virtually the same.

The formulae are illustrated with simple examples.

Read the pdf: The basics of the Fermi-Dirac and Bose-Einstein Distributions

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Bose-Einstein Condensate: data from the original paper by Wieman and Cornell. What is shown is the spatial distribution of density, the three plots being for reducing temperature: 400 nK (left), through 200 nk and finally 50 nK (right).