Single-particle state distribution

For a system of identical fermions in thermodynamic equilibrium, the average number of fermions in a single-particle state \(i\) is given by the Fermi—Dirac distribution.

Notation:

1. \(k_\text{B}\) (k_B) is boltzmann_constant.

Notes:

1. If the energy states are degenerate, i.e. two or more particles are on the same energy level, the average number of fermions can be found by multiplying by the degeneracy \(g_i\) of the energy level.

Links:

1. Wikipedia.

occupancy_of_state

Occupancy of a single-particle state \(i\).

Symbol:

N_i

Latex:

\(N_i\)

energy_of_state

Energy of state \(i\).

Symbol:

E_i

Latex:

\(E_i\)

total_chemical_potential

Total chemical potential of the system.

Symbol:

mu

Latex:

\(\mu\)

temperature

temperature of the system.

Symbol:

T

Latex:

\(T\)

Dimension:

temperature

law

N_i = 1 / (exp((E_i - mu) / (k_B * T)) + 1)

Latex:

\[N_i = \frac{1}{\exp{\left( \frac{E_i - \mu}{k_\text{B} T} \right)} + 1}\]