.. _sphx_glr_api_gallery_quantum_harmonic_oscillator:

Harmonic oscillator
--------------------

The quantum harmonic oscillator suite: Fock states, Glauber coherent
states, squeezed states, thermal broadening, an animated Fock-state
superposition, and the Wigner quasi-probability distribution in phase
space.


.. 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="Four canonical states of the 1D quantum harmonic oscillator">

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  .. image:: /api/gallery/quantum/harmonic_oscillator/images/thumb/sphx_glr_plot_harmonic_oscillator_suite_thumb.png
    :alt:

  :doc:`/api/gallery/quantum/harmonic_oscillator/plot_harmonic_oscillator_suite`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">The harmonic oscillator suite</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Builds the harmonic oscillator&#x27;s raising/lowering operators \hat a^\dagger,\hat a in a truncated Fock basis with annihilation_operator and creation_operator, verifies the algebra [\hat a,\hat a^\dagger]=1, and reads the spectrum E_n=\hbar\omega(n+\tfrac12) directly off the number_operator -- reproducing the oscillator&#x27;s energy ladder without ever solving a differential equation.">

.. only:: html

  .. image:: /api/gallery/quantum/harmonic_oscillator/images/thumb/sphx_glr_plot_ladder_operators_thumb.png
    :alt:

  :doc:`/api/gallery/quantum/harmonic_oscillator/plot_ladder_operators`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Dirac's ladder-operator method</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="The Wigner function represents a quantum state as a quasi-probability distribution over classical phase space (x,p),">

.. only:: html

  .. image:: /api/gallery/quantum/harmonic_oscillator/images/thumb/sphx_glr_plot_wigner_phase_space_thumb.png
    :alt:

  :doc:`/api/gallery/quantum/harmonic_oscillator/plot_wigner_phase_space`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Wigner phase-space quasi-probability</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/quantum/harmonic_oscillator/plot_harmonic_oscillator_suite
   /api/gallery/quantum/harmonic_oscillator/plot_ladder_operators
   /api/gallery/quantum/harmonic_oscillator/plot_wigner_phase_space