.. _sphx_glr_api_gallery_quantum_hydrogenlike:

Hydrogen-like atoms
---------------------

Hydrogen-like radial wavefunctions, radial distribution functions, and
orbital energies for 1s/2s/2p/3d, plus the exact ground-state ionization
energy.


.. 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="Schrodinger&#x27;s first 1926 paper solved his wave equation for the hydrogen atom and recovered the Bohr energies E_n\propto-1/n^2 without any quantization postulate. HydrogenLikeAtom reproduces the textbook 13.6 eV hydrogen ground-state energy exactly, and its radial wavefunctions (built from the associated Laguerre polynomials of scipy.special) are independently checked here by numerically integrating them to a normalized probability of 1.">

.. only:: html

  .. image:: /api/gallery/quantum/hydrogenlike/images/thumb/sphx_glr_plot_01_hydrogen_orbitals_thumb.png
    :alt:

  :doc:`/api/gallery/quantum/hydrogenlike/plot_01_hydrogen_orbitals`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Schrodinger's hydrogen atom: radial wavefunctions and orbital energies</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/quantum/hydrogenlike/plot_01_hydrogen_orbitals