The Fermi statistics is a direct consequence of Eq. (5.3) assuming the independence of the occupation of individual states. Using the definition
| (5.4) |
the probability for occupying the state
| (5.5) |
The electron in state
The probability that the state
| (5.6) |
since in this case the energy zero is added to the complete energy.
This
are all possibilities for a Fermion to occupy a state; consequently we find the probability for occupying the state
| (5.7) |
The Fermi statistics describes the probability to occupy a one electron state in an ensemble.
Essential for this calculation are independent electrons since for the above calculation we need that
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© J. Carstensen (Quantum Mech.)