![]() "Sommerfeld formula and Dirac's theory" (PDF). ^ - Atombau und Spektrallinien, 1921, page 520."The Kossel-Sommerfeld Theory and the Ring Atom". "Einstein's unknown insight and the problem of quantizing chaos" (PDF). ^ The Collected Papers of Albert Einstein, vol. ![]() "The quantum theory of radiation and line spectra". Nevertheless, both solutions fail to predict the Lamb shifts. This solution (using substitutions for quantum numbers) is equivalent to the solution of the Dirac equation. The Bohr–Sommerfeld model supplemented the quantized angular momentum condition of the Bohr model with an additional radial quantization condition, the Wilson– Sommerfeld quantization condition ∫ 0 T p r d q r = n h, is the fine-structure constant. Sommerfeld argued that if electronic orbits could be elliptical instead of circular, the energy of the electron would be the same, except in the presence of a magnetic field, introducing what is now known as quantum degeneracy. Bohr–Sommerfeld theory is named after Danish physicist Niels Bohr and German physicist Arnold Sommerfeld. ![]() The Bohr–Sommerfeld model (also known as the Sommerfeld model or Bohr–Sommerfeld theory) was an extension of the Bohr model to allow elliptical orbits of electrons around an atomic nucleus. Rutherford’s model introduced the nuclear model of an atom, in which he explained that a nucleus (positively charged) is surrounded by negatively charged electrons. It came into existence with the modification of Rutherford’s model of an atom. The Sommerfeld extensions of the 1913 solar system Bohr model of the hydrogen atom showing the addition of elliptical orbits to explain spectral fine structure. The Bohr model of the atom was proposed by Neil Bohr in 1915.
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