.. _sphx_glr_api_gallery_statmech_quantum_statistics:

Quantum statistics and the classical limit
--------------------------------------------

The thermal de Broglie wavelength, and how Bose-Einstein and Fermi-Dirac
statistics reduce to classical Maxwell-Boltzmann counting for ordinary
molecular gases.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

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    <div class="sphx-glr-thumbcontainer" tooltip="De Broglie&#x27;s relation \lambda=h/p, averaged over a gas&#x27;s thermal spread of momenta, gives the thermal de Broglie wavelength">

.. only:: html

  .. image:: /api/gallery/statmech/quantum_statistics/images/thumb/sphx_glr_plot_01_thermal_de_broglie_wavelength_thumb.png
    :alt:

  :doc:`/api/gallery/statmech/quantum_statistics/plot_01_thermal_de_broglie_wavelength`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">De Broglie's matter waves: the thermal wavelength of a gas</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Bose and Einstein (1924-25) and Fermi and Dirac (1926) found the mean occupancy of a single-particle state of energy \varepsilon for indistinguishable bosons and fermions:">

.. only:: html

  .. image:: /api/gallery/statmech/quantum_statistics/images/thumb/sphx_glr_plot_02_bose_einstein_fermi_dirac_limit_thumb.png
    :alt:

  :doc:`/api/gallery/statmech/quantum_statistics/plot_02_bose_einstein_fermi_dirac_limit`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Bose-Einstein and Fermi-Dirac statistics reduce to Maxwell-Boltzmann</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/statmech/quantum_statistics/plot_01_thermal_de_broglie_wavelength
   /api/gallery/statmech/quantum_statistics/plot_02_bose_einstein_fermi_dirac_limit