.. _sphx_glr_api_gallery_condensed_landau_levels:

Landau Levels
-------------

The continuum quantization of a charged particle in a uniform magnetic
field: equally spaced Landau levels, their macroscopic per-area
degeneracy, and the disorder-broadened density of states whose filling
factor sets the quantum Hall effect's plateau sequence.


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    <div class="sphx-glr-thumbcontainer" tooltip="Lev Landau solved the quantum mechanics of a charged particle in a uniform magnetic field B directly, with no lattice involved: the classically continuous cyclotron motion collapses into equally spaced, macroscopically degenerate levels E_n = \hbar\omega_c(n+1/2), landau_level_energies. Each level holds n_B states per unit area, landau_degeneracy, growing linearly with B -- the origin of Landau diamagnetism, and the reason a 2D electron gas&#x27;s Landau-level filling factor \nu=n_e/n_B (~physicskit.condensed.landau_levels.filling_factor) is the natural variable of the quantum Hall effect.">

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  :doc:`/api/gallery/condensed/landau_levels/plot_landau_levels`

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      <div class="sphx-glr-thumbnail-title">Landau's 1930 Solution: Discrete Levels from a Continuous Field</div>
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.. toctree::
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   /api/gallery/condensed/landau_levels/plot_landau_levels