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Illustration Fermi distribution graph at finite temperature

Fermi distribution graph at finite temperature
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The Fermi distribution gives the probability \( P(W) \) to encounter a fermion (for example an electron) with the energy \( W \) in a quantum mechanical gas. Here, \( \mu \) is the chemical potential corresponding to the Fermi energy at \( T = 0 \).

At absolute zero \( T = 0 \), all states to the left of \( \mu \) would be occupied: \( P = 1\) and unoccupied to the right of \( \mu \): \( P = 0 \). Multiplied by the number \(N\) of particles, the Fermi distribution \(P(W)\) tells how many particles there are at a given energy \( W \).