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:**

#. :math:`k_\text{B}` (:code:`k_B`) is :attr:`~symplyphysics.quantities.boltzmann_constant`.

**Conditions:**

#. :math:`E_i > \mu`.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_statistics#Bose%E2%80%93Einstein_distribution>`__.

.. py:currentmodule:: symplyphysics.laws.thermodynamics.bose_einstein_statistics.single_particle_state_distribution

.. py:data:: occupancy_of_state

    Occupancy of single-particle state :math:`i`.

Symbol:
    :code:`n_i`

Latex:
    :math:`n_{i}`

Dimension:
    :code:`dimensionless`


.. py:data:: energy_of_state

    :attr:`~symplyphysics.symbols.basic.energy` of single-particle state :math:`i`.

Symbol:
    :code:`E_i`

Latex:
    :math:`E_{i}`

Dimension:
    :code:`energy`


.. py:data:: total_chemical_potential

    Total :attr:`~symplyphysics.symbols.thermodynamics.chemical_potential` of the system.

Symbol:
    :code:`mu`

Latex:
    :math:`\mu`

Dimension:
    :code:`energy`


.. py:data:: temperature

    :attr:`~symplyphysics.symbols.thermodynamics.temperature` of the system.

Symbol:
    :code:`T`

Latex:
    :math:`T`

Dimension:
    :code:`temperature`


.. py:data:: law

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


    Latex:
        .. math::
            n_{i} = \frac{1}{\exp{\left(\frac{E_{i} - \mu}{k_\text{B} T} \right)} - 1}