# Illustration 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 $$W$$.