.. _sphx_glr_api_gallery_quantum_particle_in_box:

Particle in a box
------------------

1D/3D particle-in-a-box energy levels and wavefunctions, cubic-box
degeneracy, and Kuhn's free-electron model of a conjugated dye's UV-Vis
absorption wavelength.


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


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

.. thumbnail-parent-div-open

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    <div class="sphx-glr-thumbcontainer" tooltip="Plots the first few 1D particle-in-a-box wavefunctions (~chemistrykit.quantum.systems.particle_in_box.ParticleInBox1D), each offset by its own energy level, then checks the textbook 3D cubic-box degeneracy pattern (~chemistrykit.quantum.systems.particle_in_box.ParticleInBox3D). These are the simplest exact solutions of Schrodinger&#x27;s 1926 time-independent equation -\frac{\hbar^2}{2m}\nabla^2\psi=E\psi inside hard walls: quantized energies E_n=n^2h^2/8mL^2 appear from the boundary conditions alone, with no quantization postulate.">

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  .. image:: /api/gallery/quantum/particle_in_box/images/thumb/sphx_glr_plot_01_particle_in_box_thumb.png
    :alt:

  :doc:`/api/gallery/quantum/particle_in_box/plot_01_particle_in_box`

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      <div class="sphx-glr-thumbnail-title">Solving Schrodinger's equation for a particle in a box</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Hans Kuhn (1949) treated the pi electrons of a linear conjugated dye as free electrons in a one-dimensional box as long as the conjugated chain. With N pi electrons filling the box levels two at a time, the lowest absorption is the HOMO to LUMO jump, \Delta E=\frac{h^2}{8mL^2}(N+1), so a longer chain (more electrons and a longer box) absorbs at longer wavelength. conjugated_dye_absorption_wavelength implements this on top of ParticleInBox1D.">

.. only:: html

  .. image:: /api/gallery/quantum/particle_in_box/images/thumb/sphx_glr_plot_02_kuhn_free_electron_dye_thumb.png
    :alt:

  :doc:`/api/gallery/quantum/particle_in_box/plot_02_kuhn_free_electron_dye`

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      <div class="sphx-glr-thumbnail-title">Kuhn's free-electron model of conjugated dye color</div>
    </div>


.. thumbnail-parent-div-close

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    </div>


.. toctree::
   :hidden:

   /api/gallery/quantum/particle_in_box/plot_01_particle_in_box
   /api/gallery/quantum/particle_in_box/plot_02_kuhn_free_electron_dye