.. _sphx_glr_api_gallery_semiclassical_gutzwiller:

The Gutzwiller trace formula
--------------------------------

The exact one-dimensional Gutzwiller trace formula, reconstructing a
spectrum purely from a single classical periodic orbit's action and
period, and the general isolated-orbit stability amplitude used beyond
the exactly-solvable 1D case.


.. 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="Reconstructs the quantum density of states g(E)=\sum_n\delta(E-E_n) of a unit-mass, unit-frequency harmonic oscillator, V(x)=\tfrac12m\omega^2x^2 with m=\omega=\hbar=1, purely from its classical period T(E) and action S(E), with no reference to the quantum eigenstates themselves (~physicskit.semiclassical.core.gutzwiller.classical_period, gutzwiller_density_of_states). A bound 1D system has exactly one periodic orbit per energy, so Poisson-summing the discrete Bohr-Sommerfeld spectrum over its repetitions r gives an identity that is exact here -- not merely leading order in \hbar:">

.. only:: html

  .. image:: /api/gallery/semiclassical/gutzwiller/images/thumb/sphx_glr_plot_gutzwiller_trace_formula_thumb.png
    :alt:

  :doc:`/api/gallery/semiclassical/gutzwiller/plot_gutzwiller_trace_formula`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gutzwiller's trace formula</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/semiclassical/gutzwiller/plot_gutzwiller_trace_formula