# Formula Fermi distribution function Probability    Energy    Chemical potential    Temperature ## 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: $$k_{\text B} = 1.380 \, 649 \, \cdot\, 10^{-23} \, \frac{\text J}{\text K}$$.