.. _sphx_glr_api_gallery_quantum_perturbation:

Rayleigh-Schrodinger perturbation theory
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First-order perturbation theory for the quartic anharmonic oscillator,
checked against exact numerical diagonalization of the full Hamiltonian
in a truncated harmonic-oscillator basis.


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    <div class="sphx-glr-thumbcontainer" tooltip="Schrodinger&#x27;s third 1926 paper introduced his perturbation theory; here it is applied to a harmonic oscillator with an added quartic term. Checks quartic_perturbation_first_order_correction&#x27;s first-order Rayleigh-Schrodinger estimate against exact numerical diagonalization of the full anharmonic Hamiltonian (~chemistrykit.quantum.systems.perturbation.anharmonic_energy_levels, built in a truncated harmonic-oscillator basis via position_operator_matrix), and confirms that a cubic perturbation gives exactly zero first-order correction by parity.">

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  .. image:: /api/gallery/quantum/perturbation/images/thumb/sphx_glr_plot_01_anharmonic_perturbation_thumb.png
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  :doc:`/api/gallery/quantum/perturbation/plot_01_anharmonic_perturbation`

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      <div class="sphx-glr-thumbnail-title">Rayleigh-Schrodinger perturbation theory vs. exact diagonalization for the quartic oscillator</div>
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    </div>


.. toctree::
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   /api/gallery/quantum/perturbation/plot_01_anharmonic_perturbation