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HandWiki. Bohr–van Leeuwen Theorem. Encyclopedia. Available online: https://encyclopedia.pub/entry/30665 (accessed on 22 September 2026).
HandWiki. Bohr–van Leeuwen Theorem. Encyclopedia. Available at: https://encyclopedia.pub/entry/30665. Accessed September 22, 2026.
HandWiki. "Bohr–van Leeuwen Theorem" Encyclopedia, https://encyclopedia.pub/entry/30665 (accessed September 22, 2026).
HandWiki. (2022, October 21). Bohr–van Leeuwen Theorem. In Encyclopedia. https://encyclopedia.pub/entry/30665
HandWiki. "Bohr–van Leeuwen Theorem." Encyclopedia. Web. 21 October, 2022.
Bohr–van Leeuwen Theorem
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The content is sourced from: https://handwiki.org/wiki/Physics:Bohr%E2%80%93van_Leeuwen_theorem

The Bohr–van Leeuwen theorem states that when statistical mechanics and classical mechanics are applied consistently, the thermal average of the magnetization is always zero. This makes magnetism in solids solely a quantum mechanical effect and means that classical physics cannot account for diamagnetism.

statistical mechanics classical mechanics classical physics

References

  1. Bohr, Niehls (1972) [originally published as "Studier over Metallernes Elektrontheori", Københavns Universitet (1911)]. "The Doctor's Dissertation (Text and Translation)". in Rosenfeld, L.; Nielsen, J. Rud. Early Works (1905-1911). Niels Bohr Collected Works. 1. Elsevier. pp. 163, 165–393. doi:10.1016/S1876-0503(08)70015-X. ISBN 978-0-7204-1801-9.  https://dx.doi.org/10.1016%2FS1876-0503%2808%2970015-X
  2. van Leeuwen, Hendrika Johanna (1921). "Problèmes de la théorie électronique du magnétisme". Journal de Physique et le Radium 2 (12): 361–377. http://hal.archives-ouvertes.fr/jpa-00204299/en/. 
  3. van Vleck, J. H. (1932). The theory of electric and magnetic susceptibilities. Clarendon Press. ISBN 0-19-851243-0. 
  4. Aharoni, Amikam (1996). Introduction to the Theory of Ferromagnetism. Clarendon Press. pp. 6–7. ISBN 0-19-851791-2. https://archive.org/details/introductiontoth00ahar/page/6. 
  5. van Vleck, J. H. (1992). "Quantum mechanics: The key to understanding magnetism (Nobel lecture, 8 December 1977)". in Lundqvist, Stig. Nobel Lectures in Physics 1971-1980. World Scientific. ISBN 981-02-0726-3. http://nobelprize.org/nobel_prizes/physics/laureates/1977/vleck-lecture.html. 
  6. Feynman, Richard P.; Leighton, Robert B.; Sands, Matthew (2006). The Feynman Lectures on Physics. 2. p. 34-8. ISBN 978-0465024940. 
  7. Roth, Reece (1967). "Plasma Stability and the Bohr-Van Leeuwen Theorem". NASA. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19670013534_1967013534.pdf. Retrieved 2008-10-27. 
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