Arnold Johann Wilhelm Sommerfeld (5.12.1868-26.04.1951) was a German theoretical physicist and a corresponding member of the Berlin Academy of Sciences (1920). He was born in Königsberg (now Kaliningrad). He graduated from the University of Königsberg (1891). In 1891 —97 he worked at the University of Göttingen, in 1897—1900 he was professor at the Mining Academy in Clausthal, in 1900 —06 at the Higher Technical School in Aachen and in 1906 — 38 at the University of Munich.
His work concerned the quantum theory of the atom, spectroscopy, the quantum theory of metals and mathematical physics. On the basis of Maxwell's theory he gave in 1894 a rigorous solution of the problem of optical diffraction for the case of a screen in the form of an infinite half-plane bounded by a straight edge, and in 1909 he solved the problem of the radiation of a vertical dipole.
In the quantum theory of spectral lines, starting from Bohr's model of the atom, he brought about a synthesis of quantum theory and relativity, developing (1915—16) the quantum theory of elliptical orbits (the Bohr–Sommerfeld theory). He introduced the radial and azimuthal quantum numbers and explained the fine structure of the hydrogen and X-ray spectra. He developed the theory of the fine structure of the hydrogen spectrum, introducing the fine-structure constant. In 1916, together with P. Debye, he constructed the quantum theory of the Zeeman effect and introduced the magnetic quantum number, and in 1919, with W. Kossel, he established the spectroscopic displacement law. He derived formulas for the intensities of multiplet lines. In 1920 he introduced the inner quantum number and gave the selection rules for doublet and triplet spectra.
In 1931 he developed the theory of the bremsstrahlung of electrons moving at a speed considerably less than the speed of light. Assuming in 1928 that the free electrons in metals behave like a rarefied gas obeying Fermi–Dirac statistics, he developed the theory of the metallic state (the quantum electron theory of metals) and obtained a number of important results here.
The author of textbooks on theoretical physics. The founder of the Munich school of theoretical physics (W. Heisenberg, W. Pauli, P. Debye, H. Bethe, G. Wentzel, W. Heitler, W. Kossel, A. Landé, H. Fröhlich, O. Laporte, W. Rubinowicz, P. Ewald and others). A member of many academies of sciences and scientific societies, in particular a foreign member of the USSR Academy of Sciences (1929).