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      "statement": "# Landau: quantum orbital motion gives free electrons a magnetic response\n\nLandau counts the partly discrete quantum energies of nonrelativistic electrons in a uniform magnetic field and derives a nonzero orbital diamagnetic response, distinct from spin paramagnetism, with an explicit smooth-field approximation and separate conjectures about real materials and transport.\n\nA magnetic field does more than bend the path of an electron. In quantum mechanics it changes the allowed energies of motion across the field. Landau used those energy levels, including how many states each level represents, to calculate a magnetic response that an ordinary continuous classical calculation misses. The orbital contribution opposes the field. Spin produces a separate contribution, so this does not mean that every electron gas or metal is diamagnetic overall. The paper makes the model and its limits visible: smooth weak-field calculations differ from very cold, strongly quantized conditions; real crystal lattices and impurities need further work. It gives researchers a way to connect quantum state counting to macroscopic magnetism while leaving later experiments and transport theories their own credit.\n\n## Scientific scope\n\nThe model concerns a quantum electron gas in the stated magnetic-field, thermodynamic and statistical setting. Orbital quantization and spin contributions must be distinguished. Interactions, lattice effects and arbitrary material susceptibility are outside the idealized calculation. Later oscillation theory and experiments remain separate.\n\n## People and systems\n\nL. Landau\n\n\n\n## Original sources\n\n- [L. Landau, Diamagnetismus der Metalle; exact1930 original hosted in Gilles Montambaux physics-history collection](https://gilles.montambaux.com/files/histoire-physique/Landau-1930.pdf)\n- [Publisher-deposited identity for the exact1930 Landau diamagnetism paper](https://api.crossref.org/works/10.1007%2FBF01397213)\n- [Montambaux2020 two-page physics history: magnetic levels, diamagnetism and quantum oscillations](https://gilles.montambaux.com/files/histoire-physique/notes/Landau-levels.pdf)\n",
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