Spectral energy density at high frequency limit
===============================================

*Wien's approximation*, also known as *Wien distribution law*, describes the spectrum of blackbody
thermal radiation. It accurately describes short-wavelength (i.e. high-frequency) spectrum of
thermal emission, but fails to do that for long-wavelength (i.e. low-frequency) emission.

**Notation:**

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

**Conditions:**

#. The black body is isolated from the environment.
#. :math:`h \nu \gg k_\text{B} T`, i.e. photon energy is much greater than thermal energy.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Wien_approximation>`__.

.. py:currentmodule:: symplyphysics.laws.waves.blackbody_radiation.spectral_energy_density_in_high_frequency_limit

.. py:data:: spectral_energy_density

    :attr:`~symplyphysics.symbols.basic.spectral_energy_density`.

Symbol:
    :code:`w_f`

Latex:
    :math:`w_{f}`

Dimension:
    :code:`energy/(frequency*volume)`


.. py:data:: radiation_frequency

    :attr:`~symplyphysics.symbols.classical_mechanics.temporal_frequency` of the radiation.

Symbol:
    :code:`f`

Latex:
    :math:`f`

Dimension:
    :code:`frequency`


.. py:data:: equilibrium_temperature

    Equilibrium :attr:`~symplyphysics.symbols.thermodynamics.temperature` of the ensemble.

Symbol:
    :code:`T`

Latex:
    :math:`T`

Dimension:
    :code:`temperature`


.. py:data:: law

    :code:`w_f = 8 * pi * h * f^3 / c^3 * exp(-h * f / (k_B * T))`


    Latex:
        .. math::
            w_{f} = \frac{8 \pi h f^{3}}{c^{3}} \exp{\left(- \frac{h f}{k_\text{B} T} \right)}