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Currently Playing: Quantum numbers weren't supposed to do this

Buy me a coffee and support the channel: https://ko-fi.com/jkzero Become a member and get access to the Supplementary Notes with all the equations and extra content https://ko-fi.com/jkzero/tiers In 1921 physicist Alfred Landé found a formula that finally matched the spectral lines of the anomalous Zeeman effect, but it demanded some quantum numbers take half-integer values. This is the story of how mathematics forced reluctant physicists to accept an idea they had every reason to resist. [Related videos] ∘ Planck's solution of blackbody radiation https://youtu.be/gXeAp_lyj9s ∘ Quantum theory of the normal Zeeman effect https://youtu.be/DetAXY2cpzM ∘ Sommerfeld and the fine-structure constant https://youtu.be/H4ZnVpiQTDw ∘ When helium broke quantum theory https://youtu.be/EqgbfdesMG4 ∘ Playlist video series on Quantum Physics https://www.youtube.com/playlist?list=PL_UV-wQj1lvVxch-RPQIUOHX88eeNGzVH [References] [1] T. Preston, "Radiation phenomena in a strong magnetic field," Sc. Trans. R. Dub. Soc. 6, 385 (1898) [2] J. Stark and H. Kirschbaum, "Beobachtungen über den Effekt des elektrischen Feldes auf Spektrallinien. III. Abhängigkeit von der Feldstärke," Ann. Phys. 348: 991-1016 (1914) [3] F. Paschen and E. Back, "Normale und anomale Zeemaneffekte," Ann. Phys. 344(15) 897-932 (1912) [4] P. Zeeman, "Researches in magneto-optics, with special reference to the magnetic resolution of spectrum lines," London, Macmillan (1913) [5] W. Voigt, Ann. Phys. 346, 403 (1913) [6] W. Voigt, "Über das elektrische Analogon des Zeemaneffectes," Ann. Phys., 309: 197-208 (1901) [7] N. Bohr, "On the constitution of atoms and molecules," Philos. Mag. 26, 151: 1 (1913) [8] A. Sommerfeld, "Atomic structure and spectral lines," (H. L. Brose, Trans.). Methuen & Co. (1923) [9] A. Sommerfeld, "Allgemeine spektroskopische Gesetze insbesondere ein magnetooptischer Zerlegungssatz," Ann. Phys. 63, 221 (1920) [10] M. Born interviewed by T. S. Kuhn and F. Hund, Session III, AIP (1962) https://repository.aip.org/node/127806 [11] A. Rubinowicz, "Bohrsche Frequenzbedingung und Erhaltung des Impulsmomentes, Teil I" Phys. Z. 19, 441-445 (1918) [12] A. Rubinowicz, "Bohrsche Frequenzbedingung und Erhaltung des Impulsmomentes, Teil II" Phys. Z. 19, 465-474 (1918) [13] P. S. Epstein "Zur Theorie des Starkeffekts," Ann. Phys. 50, 489-521 (1916) [14] A. Landé, "Über den anomalen Zeemaneffekt (I.Teil)," Z. Phys. 5 231–241 (1921) [15] P. Forman, "Alfred Landé and the Anomalous Zeeman Effect, 1919-1921," Hist. Stud. Phys. Sci. 2, 153–261 (1970) [16] A. Sommerfeld, "Quantentheoretische Umdeutung der Voigtschen Theorie des anomalen Zeeman-Effektes vom D-Linientypus," Z. Phys. 8(1), 257–297 (1922) [17] W. Heisenberg, "Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen," Z. Phys. 33, 879 (1925) [Credits] M. Planck, public domain A. Einstein, public domain P. Debye, public domain A. Landé, public domain Periodic table, GSI Fraunhofer's original spectrum, by J. Fraunhofer under CC BY-SA 4.0 Sodium spectrum, NIST A. Michelson, public domain E. Morley, public domain Pieter Zeeman, public domain T. Preston, public domain Anode Ray Tube by Kkmurray under CC BY-SA 3.0 J. Stark, public domain Physikalisches Institut der Universität Tübingen by Deutsche Digitale Bibliothek E. Back, public domain F. Paschen, public domain Electromagnet model by Amanjosan2008 under CC BY-SA 4.0 H. Lorentz, public domain A. Sommerfeld, public domain P. S. Epstein, public domain K. Schwarzschild, public domain P. Debye, public domain W. Voigt, public domain Bohr and Planck, AIP Rudolphine Tables by J. Kepler, public domain M. Born, public domain P. Dirac, public domain Heisenberg, public domain Sommerfeld and Pauli, AIP W. Heisenberg, AIP AIP: American Institute of Physics, Emilio Segrè Visual Archives CC BY-SA 3.0: https://creativecommons.org/licenses/by-sa/3.0/deed.en CC BY-SA 4.0: https://creativecommons.org/licenses/by-sa/4.0/deed.en