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Formula Fermi distribution function Probability    Energy    Chemical potential    Temperature   

Formula
Formula: Fermi distribution function

Probability

Unit
The occupation probability indicates the probability \(P\) that a state with energy \( W \) is occupied at temperature \( T \). At absolute zero (\(T=0 \, \text{K}\)), the probability that the state with energy \( W \) is occupied is exactly 50%: \( P(W) ~=~ \frac{1}{2}\).

Energy

Unit
Energy state which can be occupied by a fermion, for example by an electron.

Chemical potential

Unit
Chemical potential gives the change of the internal energy when the particle number of the Fermi gas (e.g. free electron gas) changes. At \( T=0 \, \text{K} \) the chemical potential correspons to the Fermi energy: \( \mu = W_{\text F} \).

Temperature

Unit
Absolute temperature of the Fermi gas, for example a free electron gas in a metal.

Boltzmann constant

Unit
Boltzmann constant is a natural constant, which is used more often in statistical physics and thermodynamics. It has the value: \( k_{\text B} = 1.380 \, 649 \, \cdot\, 10^{-23} \, \frac{\text J}{\text K} \).