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Landau: quantum orbital motion gives free electrons a magnetic response

Contribution grade

Quantum magnetism · Quantum magnetism

Reference score230,000Provisional editorial estimate of this exact contribution; its grade is assessed separately.

What changed

Landau 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.

Scientific scope

Landau 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. The 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.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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