The fine structure of the atom

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Development of the Bohr-Sommerfeld atomic model, which extended Bohr's model by incorporating elliptical orbits and relativistic corrections, in addition to introducing the fine-structure constant. This pivotal model finally explained the mysterious fine-structure splitting of spectral lines discovered by the second Michelson-Morley experiment and sets the foundation for modern quantum mechanics.

[Extra materials]
∘ Elliptical orbits in the phase-space quantization https://arxiv.org/abs/1605.08027

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[References]
∘ P. Zeeman, Nature 55, 347 (1897)
∘ A.A. Michelson and E. W. Morley, "On a method of making the wave-length of sodium light the actual practical standard of length," Phil. Mag. 24, 463 (1887)
∘ N. Bohr, "On the Effect of Electric and Magnetic Fields on Spectral Lines," Phil. Mag. 27, 506 (1914)
∘ A. Sommerfeld, "Zur Theorie der Balmerschen Serie," Klasse der K.B. Akademie der Wissenschaften zu München, 425 (1915)
∘ W. Wilson, Phil. Mag. 29, 795 (1915)
∘ L.A. de Castro, C.A. Brasil, and R. Napolitano, "Elliptical orbits in the phase-space quantization," Rev. Bras. Ensino Fís. 38, 3 (2016) https://doi.org/10.1590/1806-9126-RBE...
∘ A. Sommerfeld, "Die Feinstruktur der Wasserstoff- und der Wasserstoff-ähnlichen Linien," Klasse der K.B. Akademie der
Wissenschaften zu München, 459 (1916)
∘ A. Sommerfeld, "Zur Quantentheorie der Spektrallinien," Ann. Phys. 51, 1-94, 125-167 (1916)
∘ F. Paschen, Bohrs Heliumlinien, Ann. Phys. 50, 901 (1916)


[Credits]
A. Sommerfeld , by Bain News Service, public domain
Wilhelm Lenz, AIP
Pieter Zeeman, AIP
Paul Langevin, by H. Manuel under CC BY 4.0
Maurice de Broglie, by Studio Harcourt under CC BY-SA 4.0
Louis de Broglie, public domain
Visible spectrum of hydrogen, by J. Homann under CC BY-SA 3.0
Zeeman splitting, by P.Zeeman, public domain
J. Stark, by A.B. Lagrelius, public domain
A. Michelson, public domain
E. Morley, public domain
Michelson-Morley experiment, by CWRU, public domain
Werner Heisenberg, AIP
Erwin Schrödinger, AIP
Friedrich Paschen, public domain
High voltage experimental physics demonstration, by Hans on Pixabay
Electron transitions of Hydrogen, by OrangeDog/Szdori under CC BY-SA 3.0
Karl Schwarzschild, public domain
Black hole visualization, by NASA/J.Schnittman, public domain
WWI communications, public domain
William Wilson, by T.Carrick under CC BY-SA 3.0
Visible Spectrum of Hydrogen, by J. Homann under CC BY-SA 3.0
Perihelion precession of Mercury, by R.Zenz, public domain
Sommerfeld orbits, by CielProfond under CC BY-SA 4.0
Werner Heisenberg, AIP



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