Single particle state distribution

Occupancy of a single-particle state of bosons is the probability of a single boson to occupy a state with a certain amount of energy. The occupancy depends on the energy of the state and the temperature and the chemical potential of the system.

Notation:

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

Conditions:

1. \(E_i > \mu\).

Links:

1. Wikipedia.

occupancy_of_state

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

Symbol:

n_i

Latex:

\(n_{i}\)

Dimension:

dimensionless

energy_of_state

energy of single-particle state \(i\).

Symbol:

E_i

Latex:

\(E_{i}\)

Dimension:

energy

total_chemical_potential

Total chemical_potential of the system.

Symbol:

mu

Latex:

\(\mu\)

Dimension:

energy

temperature

temperature of the system.

Symbol:

T

Latex:

\(T\)

Dimension:

temperature

law

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

Latex:

\[n_{i} = \frac{1}{\exp{\left(\frac{E_{i} - \mu}{k_\text{B} T} \right)} - 1}\]