.. _sphx_glr_api_gallery_quantum_wave_packets:

Wave packets
------------

Non-stationary wave dynamics: free dispersion (with an animated view of
the spreading), twin-slit interference, quantum revivals in an infinite
well, Ehrenfest's theorem in an anharmonic potential, and a phase-colored
animation of double-well tunneling.


.. raw:: html

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


.. raw:: html

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

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Builds a free Gaussian wavepacket carrying de Broglie&#x27;s traveling-wave factor e^{ik_0 x} via free_gaussian_wavepacket, and verifies that its momentum-space density peaks exactly at p_0=\hbar k_0, so the associated wavelength is de Broglie&#x27;s \lambda = h/p.">

.. only:: html

  .. image:: /api/gallery/quantum/wave_packets/images/thumb/sphx_glr_plot_de_broglie_wavepacket_thumb.png
    :alt:

  :doc:`/api/gallery/quantum/wave_packets/plot_de_broglie_wavepacket`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">De Broglie's matter wave</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Ehrenfest&#x27;s theorem states that quantum expectation values obey the classical equations of motion exactly:">

.. only:: html

  .. image:: /api/gallery/quantum/wave_packets/images/thumb/sphx_glr_plot_ehrenfest_theorem_thumb.png
    :alt:

  :doc:`/api/gallery/quantum/wave_packets/plot_ehrenfest_theorem`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Ehrenfest's theorem in an anharmonic well</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Propagates a wavepacket initially localized in the left well of a double well V(x) = \lambda(x^2-a^2)^2 with the real FFT split-operator solver (not the two-level analytic shortcut used in the double-well example), and renders it with animate_density&#x27;s HSV phase coloring: hue tracks the local complex phase \arg\psi(x,t), so the accumulating phase gradient as the packet tunnels back and forth is directly visible, not just the probability density.">

.. only:: html

  .. image:: /api/gallery/quantum/wave_packets/images/thumb/sphx_glr_plot_phase_colored_animation_thumb.gif
    :alt:

  :doc:`/api/gallery/quantum/wave_packets/plot_phase_colored_animation`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">A phase-colored tunneling animation</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Three non-stationary phenomena governed by the time-dependent Schrodinger equation, each solved via its own exact analytic route rather than direct numerical propagation. A free Gaussian wavepacket keeps its Gaussian shape but spreads as it travels, its width growing as">

.. only:: html

  .. image:: /api/gallery/quantum/wave_packets/images/thumb/sphx_glr_plot_wave_packet_dynamics_thumb.png
    :alt:

  :doc:`/api/gallery/quantum/wave_packets/plot_wave_packet_dynamics`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Dispersion, twin-slit interference, and quantum revivals</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/quantum/wave_packets/plot_de_broglie_wavepacket
   /api/gallery/quantum/wave_packets/plot_ehrenfest_theorem
   /api/gallery/quantum/wave_packets/plot_phase_colored_animation
   /api/gallery/quantum/wave_packets/plot_wave_packet_dynamics