Quantum Statistics

In the case of high densities and/or low temperatures,

the wave functions of the various particles (partly) overlap.

This gives rise to specific quantum effects which influence

the distributions of the elementary particles.

Such situations are quite frequently encountered when cosmic

phenomena are being investigated, like for instance neutron

stars, the cosmic microwave background radiation or the sites

where cosmic rays are produced.

To enable a proper description and understanding of these situations,

the Fermi-Dirac and Bose-Einstein statistical distributions are

derived from first principles.

Using the Fermi-Dirac and Bose-Einstein statistics, the concept of

Quantum Mechanical Phase-Space is introduced and the distribution

functions for a Free Electron Gas and Photon Gas are derived explicitly.

The latter is used in an application to determine the mean free path

of high-energy protons that are traveling through the cosmic microwave

background radiation. This gives rise to the so called GZK cutoff

for the most energetic cosmic rays.

Lecture Notes :

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