March 2014
Intermediate to advanced
624 pages
26h 33m
English
In this section, we will give a simplified derivation of Fermi–Dirac statistics. We will not go through all the details, but will instead point out the physical assumptions involved. The distribution function is determined by calculating the number of distinct ways (Wk ) we can put nk indistinguishable electrons in gk states at an energy level Ek, subject to the Pauli exclusion principle.
The assumptions are:
Each allowed state has a maximum of one electron (Pauli principle).
The probability of occupancy of each allowed (degenerate) quantum state is the same.
All electrons are indistinguishable.
The number of distinct ways we can put the electrons in a particular level is
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