Thermal de Broglie wavelength
=============================

The thermal de Broglie wavelength can be roughly described as the average de Broglie wavelength
of particles in an ideal gas at a specified temperature. When compared to average inter-particle
spacing in the gas, it can be used to tell if the gas can be considered to be a classical or
Maxwell-Boltzmann gas, in which case the thermal wavelength must be much smaller than the average
inter-particle spacing. Otherwise, quantum effects must be taken into account.

**Notation:**

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

**Links:**

#. `Wikipedia, see last formula in paragraph <https://en.wikipedia.org/wiki/Thermal_de_Broglie_wavelength#Massive_particles>`__.

.. py:currentmodule:: symplyphysics.definitions.thermal_de_broglie_wavelength

.. py:data:: thermal_wavelength

    Thermal de Broglie :attr:`~symplyphysics.symbols.classical_mechanics.wavelength` of the gas.

Symbol:
    :code:`lambda`

Latex:
    :math:`\lambda`

Dimension:
    :code:`length`


.. py:data:: mass

    :attr:`~symplyphysics.symbols.basic.mass` of a single gas particle.

Symbol:
    :code:`m`

Latex:
    :math:`m`

Dimension:
    :code:`mass`


.. py:data:: temperature

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

Symbol:
    :code:`T`

Latex:
    :math:`T`

Dimension:
    :code:`temperature`


.. py:data:: definition

    :code:`lambda = hbar * sqrt(2 * pi / (m * k_B * T))`


    Latex:
        .. math::
            \lambda = \hbar \sqrt{\frac{2 \pi}{m k_\text{B} T}}