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  "body": "\n## Summary\n\nAnderson localization is the absence of wave transport in a disordered medium.\nMathematically, a random [[Schrödinger operator|89AA6XJY5K]] has, in some energy range, only eigenvalues, with eigenfunctions that decay exponentially away from a centre.\nIt was proposed by the physicist P. W. Anderson in 1958 for electrons in a random lattice.\nIt is proved for the one-dimensional Anderson model at all energies and in every dimension at large disorder.\n\n## Explanations\n\n### L1 human\n\nImagine a wave moving through a crystal whose atoms have random energies.\nEach atom scatters the wave a little, and the scattered pieces interfere.\nIn a strongly disordered medium the interference is destructive on average, and the wave stays trapped near where it started.\nFor an electron this means the material does not conduct: the states are localized.\nMathematically, localized states are eigenvectors of the energy operator that are concentrated near one point and very small far away.\n",
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